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MATHEMATICS LIBRARY 
THE UNIVERSITY 


OF ILLINOIS 
LIBRARY 


The 
Frank Hall collection 
of arithmetics, 
presented by Professor 
H. L. Rietz of the 
University of Iowa. | 


SHOFE Sls 
I08Q | 
VS 


aT HEMATECS Ly 
Return this book on or before the 
Latest Date stamped below. 


University of Illinois Library 


L161—H41 


THE 


SOUTHWORTH-STONE ARITHMETIC 


A RATIONAL METHOD 


BOOK Ill. FOR ADVANCED GRADES 


GORDON A. SOUTHWORTH 
SUPERINTENDENT OF SCHOOLS, SOMERVILLE, MASS. 
AND 


JOHN C. STONE, A.M. 


ASSOCIATE PROFESSOR OF MATHEMATICS, STATE NORMAL COLLEGE, 
YPSILANTI, MICHIGAN 


OU TOAN AAXA TOAD 


BENJ. H. SANBORN & CO. 
BOSTON NEW YORK CHICAGO 


THE 


SOUTHWORTH-STONE ARITHMETIC. 


BOOK I. PRIMARY. 
BOOK II. INTERMEDIATE. 
BOOK III. ADVANCED. 


WITH OR WITHOUT ANSWERS. 


COPYRIGHT, 1904, BY 


GORDON A. SOUTHWORTH anp JOHN C. STONE. 


Norwood 48ress 
J.S. Cushing & Co.— Berwick & Smith Co. 
Norwood, Mass., U.S.A. 


MATHEMATICS LIBRARY 


PREFACE 


“The Southworth-Stone Arithmetic” is a graded series of three 
Books each separated into two Parts. The series is designed to 
cover the work of all the elementary grades in which a text-book is 
commonly used, beginning with the third-year grade and ending with 
the last year below the high school. 

The books have been prepared not by theorists to exploit their 
peculiar notions, but by teachers of long and successful experience. 
They follow the order of subjects and the lines of development 
established by the highest educational authorities. 

No attempt has been made to follow the so-called “spiral plan,” 
now decadent; each grade, however, thoroughly reviews and carries 
forward the work of the preceding grades, new topics being in- 
troduced in order to stimulate the interest of the student and to 
develop his power. 

In the presentation of subjects the inductive method has been 
employed throughout in a way that calls for study and effort and 
secures that mathematical training that never comes by mechanical 
figuring and imitation. This logical development of subjects dif- 
ferentiates the series from mere books of problems. 

To secure skill and proficiency in the more important na biecs, 7 
abundant exercises for drill and practice have been provided. A 
profusion of oral and written problems is given in about equal pro- 
portion. The number to be used must depend upon the need of the 
student. It will be found that fewer problems carefully solved and 
logically analyzed will be more valuable than many mechanically 
performed. 

Many subjects heretofore treated in arithmetics have been 


omitted as non-essential or beyond the legitimate work of the ele- 
ili 


464010 


iv PREFACE 


mentary schools. Enough has been given, however, to meet the 
demands of business and to furnish the requisite mental discipline. 

The methods employed in all the books of the series have been 
tested in manuscript in the model or training classes in the State 
Normal College at Ypsilanti, Michigan. The authors acknowledge 
their indebtedness to Miss Abigail Roe and Miss Mary Steagall and 
other teachers in that institution for valuable suggestions growing 
out of such tests. Especial thanks are due to President L. H. Jones 
of the College, for his counsel as the work has progressed and for his 
aid in making the books worthy of adoption and use. 


Part I of this Third Book of “The Southworth-Stone Arithmetic ” 
Series presents, with more prominent reference to principles, a brief 
review of the fundamental processes, common fractions, ratio, and 
decimals. It gives a complete presentation of mensuration and its 
applications to the six quadrilaterals, to triangles, to circles, to 
rectangular prisms, and to the cylinder. Tables of weights and 
measures in full are given for reference. Problems, both oral and 
written, abound. 

Part II takes up the subject of percentage analytically and ina 
way to show that it is only a restatement of principles and pro- 
cesses already familiar, under new names. Its application to busi- 
ness problems, insurance, commission, stocks, bonds, taxes, etc., is 
fully illustrated. Interest,— simple, exact, compound, — partial 
payments, bank discount, exchange, proportion, square root and its 
applications, mensuration of pyramids, cones, spheres, and similar 
triangles, the metric system, longitude and time, are followed by 
a large number of practical problems that afford a complete review 
of all subjects. Definitions of all technical terms used in the book 


are alphabetically arranged for easy reference and review. (See 
Index.) 


INDEX 


PAGE 

Accounts, ha pss 
Addition, of integers, 8, 9 
Of fractions, 46-49 
Of decimals, 75 
Angles and arcs, 87, 88 
Bank check, 199 
Bank discount, 184-189 
Of interest-bearing notes, 188 
Bills of exchange, 200-201 
Bonds, 195-197 
Business forms, 15, 169, 184, 185, 190, 
199, 200 

Cancellations, 53 
Cash account, 15 
Check, 199 
Circles, 102-105 
Commission, 163-166 
Comparison of numbers, 35, 36, 38, 
61-63 

Complex fractions, 57 
Compound interest, 182-183 
Cones, 228-230 
Customs, 180-181 
Cylinder, 115, 116 
Decimals, 71-81 
Decimal system, 2 
Definitions, 280 
Denominate numbers, 37, 40, 70, 86 
Difference between dates, 151 
Discount, bank, 184-189 
Trade or commercial, 157-160 


Successive, 159 


Division, of integers, 23-26 
Of fractions, 55-57 
Of decimals, 78, 79 

Drafts, 199-201 

Duties, 180-181 

Equations, 5) 

Exact interest, 153 

Exchange, 198-202 


PaGcE 

Factoring, 45 
Fractions, common, 4,5 
Complex, 57 
Decimal, 5, 71-81 
Changes in form of, 42-44, 74, 79 
Added and subtracted, 46-49 
Multiplied, 33, 50-53 
Divided, 55-57 
Practice table, 54, 58 
Greatest common divisor, 44 
Insurance, 161, 162 
Interest, general method, 82, 83 
Bankers’ method, 146-149 
One dollar method, 149, 150 
Choice of methods, 152, 154 
Compound, 182-183 
Drill table, 156 
Exact, 153 
Legal rates, 149 
Land measure, 95, 96, 236 
Leap years, 129 
Least common multiple, 47, 48 
Longitude and time, 245-247 


Measurements of — 

Ares and Angles, 87, 88; Circles, 
102-105 ; Cones, 226, 227 ; Cylin- 
ders, 115, 116, 226-227 ; Hypote- 
nuse, 218+ Land,.95, 96,7 236: 
Lines, 8, 87 ; Lumber, 113 ; Pyra- 
mids, 223-225; Prisms, 109-111, 
114, 2238-225.; Rectangles, 90-96 ; 
Rhomboids, 100; Rhombus, 106 ; 
Roofs, 93; Surfaces, 86 ; Spheres, 
228-230 ; Trapeziums, 99; Trape- 
zoids, 100; Triangles, 97-99; 
Wood, 112 

Mensuration (see Measurements). 


Metric system, 235-244 
Mixed numbers, 33 
Multiples, 47 


vl INDEX 


PAGE 
Multiplication, of integers, 17-21 
Of fractions, 33, 50-53 
Of decimals, {homer tr 
Notation, integers, 1-8 
Decimal, 6, 71-72 
Notes, promissory, 169-177 
Discounted, 184-189 
Partial payments of, U.S, rule, 
172-177 
Numbers, kinds of, 6, 44 
Divisibility of, 45 
Numeration, 3, 71-72 
Partial payments, 172-177 
Percentage, 63, 181-205 


Business problems, 141, 144, 145; 
Bonds, 195-197 ; Commission, 165- 
166; Duties, 180-181; Exchange, 
198-202; Insurance, 161, 162; 
Profit and loss, 141, 144, 145; 
Stocks, 190-194; Taxes, 178-179; 
Trade discount, 157-160. 

Powers, 211 
Principles of — 

Cancellation, 53; Decimal system, 
73, 78; Division, 24; Fractions, 
43, 46, 50; Interest, 147; Multi- 
plication, 18; Partial payments, 
178, 175; Proportion, 206; Re- 
duction of fractions, 43; Right 
triangle, 218. 


Square root, 211-222 


Prisms, 109-111, 114, 228-225 
Profit and loss, 141, 144, 145 
Proportion, 206-210 
Pyramid, 223-225 
Quadrilaterals, 88-90 
Ratio, 35, 36, 88, 61-63 | 
Rectangles, 90-96 
Revenues, government, 180-181 


Review Exercises in — 
Fundamental rules, 138, 14, 32, 34, 
39, 41 


Fractions, 41, 42, 59, 60, 64-70 


Decimals, 


PAGE 


80, 81 


Measurements, 91-96, 101, 107, 108, 
117-121, 237, 238 


Percentage, 


Miscellaneous, 


167-168, 203-205 
Interest and bank discount, 
122-128, 248-279 


189 


From examinations, 260-279 
Square root, 221, 222 
Rhomboids, 100 
Right triangles, 218, 219 
Roots, 211-222 
Rule of three, 207 
Short processes, 27, 28 
Signs, use of, 29 
Similar surfaces, 231 
Similar triangles, 234, 235 
Similar volumes, 232, 233 
Spheres, 228-230 
Square root, 211-222 
Statement of problems, 22, 31 
Stocks, 190-194 
Subtraction, of integers, 10-12 
Of fractions, 46-49 
Of decimals, 75 
Successive discounts, 159 
Surveyor’s measure, 236 
Tables for drill — 
Fundamental rules, 12 
Fractions, 54, 58 
Percentage, 140 
Interest, 156 
Tables of weights and measures, 129, 
130 
Metric system, 235-244 
Taxes, 178-179 
Time between dates, 161 
Trade discount, 157-160 
Trapeziums, 90 
Trapezoids, 90 
Triangles, 97-99, 218-220 
United States money, 7 
Weights and measures, 129, 130 
Wood measure, 112 


THE SOUTHWORTH-STONE ARITHMETIC 


THIRD BOOK 


dedaWiaidl a 


NUMBERS: USE, NAMES, AND NOTATION 


1. What need of numbers has a merchant? A carpenter? A 
farmer? A tailor? A surveyor? A capitalist? 


2. 


oanonnrt Oona F w 


10. 


What does thirteen mean ? Fourteen ? 

Explain the meaning of all the numbers from 13 to 19. 

What does the syllable -teen mean ? 

What does twenty mean? Thirty? Forty? 

What does the syllable -ty mean ? 

What do we cail 10 tens? 10 hundreds? 1000 thousands ? 
Mention some numbers that are named by a single word. 
Show how other numbers are named. Give some examples. 


How many different figures are used in expressing numbers 


by the system we use ? 


ll. 


How is it that all numbers can be expressed by only ten 


figures ? 


Our system of writing numbers is called the Arabic system, for the 
system was first introduced into Europe by the Arabs, and they were 
supposed to be the discoverers. Modern historical research shows 
that the Hindus were the real discoverers, and hence the system is 
sometimes called the Hindu system. 


1 


ae REVIEW: A DECIMAL SYSTEM Oral 


1. In 5, 50, 500, 5000, how does the 5 change in value ? 
2. What value does the zero have? Why is it used ? 
3. The value of a figure depends upon what two things ? 


4. What does the figure in the first order at the right represent ? 
In the second order? In the third ? 


5. In 707,070 name the units in each order. 


6. Compare the value of each 7 with that of the other 7’s. ' 

7. 100 ones=1 ——. 10 ——=1 million. 
hundreds=10 thousands. 10——=1 hundred thousand. 
hundreds=50 tens. 10 -—- =] ten thousand. 


8. How many units of any order does it take to make one unit 
of the next order at the left ? 


9. In our money system how many cents make onedime? How 
many dimes make one dollar ? 


Since in our system of writing numbers, and in our money 
system, ten units of any order make one of the next higher, we call 


these decimal systems. 
Remember that decem is Latin for “ ten.’’ 


In a decimal system ten units of any order make one of the next 
higher order. 


10. In 347,900,903,531 what is the order of each 9? Compare 
their values. 


11. How do the three 3’s compare in value ? 
12. What is the use of the zeros ? 
13. Why is this number grouped into periods of threes ? 


14. Name each period, beginning with the lowest. 


REVIEW: READING AND WRITING NUMBERS 3 


Read without using the word “and” : — 


1. 4,705 6,137,008 42,200,020 10,063,005 
2. 27,003 3,000,975 34,003,007 16,100,005 
3. 195,006 600,001 93,040,075 26,013,200 
4. 70,590 17,080,005 349,000,672 85,003,017 
5. 100,054 2,008,500 34,206,000,127 93,090,006 


The next three periods after millions are billions, trillions, quad- 
rillions. 

6. Mention something counted in millions. Can you think of 
any use for billions, trillions, or larger numbers ? 


Read the following : — 
7. The population of New York State in 1900 was 7,268,894. 
The school enrollment of the state was 1,242,416. 
8. The total population of the United States in 1900 was 
84,233,069. 


9. In the twelve months ending with March, 1903, the exports 
of the United States were $1,414,786,954, against $1,001,596,683 of 
imports. 

10. In 1900 the United States produced 2,105,102,516 bushels of 
corn valued at $751,220,034. 


11. Write the largest possible number, using these six figures 
only: 0; 0; 2,.9,.3,.7.°' Tell why you put each figure in the order 
that you did. 


Write in figures, putting a comma after each period before filling 
another : — 


12. 3 billion, 108 thousand,11. 15. Ten billion, two million, sixty. 
13. 828 million, 7 thousand, 9. 16. One less than a billion. 
14. 200 million, 76. . 17. The sum of 18000, 200000, 520. 


4 REVIEW : UNITS, FRACTIONAL AND INTEGRAL Oral 


1. In the number 6 ft., what is the unit of measure? 


2. Name the unit in each of the following : — 
6bu.; 12 in.3! 60 ft); 9 eb 
Any quantity with which another quantity of the same kind is 
compared or measured is considered a unit. 


3. What are numbers called whose units are whole things? 
ee 
4. Numbers whose units are parts of whole things are what? 


5. How many fractional units are made by cutting a thing into 


three equal parts? Into four? How do these units compare in 


size? Then which is larger, 3 or 2? Why? 


6. Give the largest possible fractional unit. Explain your answer. 
7. Give avery small fractional unit. How many of these make 1? 


Write the fraction denoting the following : — 


NuMBER OF UNITS THE FRACTIONAL UNIT 
8. 3 one fourth. 
9. 5 one eighth. 
10. 2 one fifth. 
11; 7 one ninth. 


12. Illustrate the following numbers by drawings : — 
on wile. 2 ak bts 
2)i) pliGig wel eleG? peeedr li Beer Gennes 
13. Read the numbers in the order of their size, the largest first. 
14. How many of each would make 1? 
15. Upon what does their size depend ? 
16. How many fractional units in 2, 75, H, 7%, 14? 
17. How many of each size make 1? Which of the fractions are 
nearest 1 ? 


Oral REVIEW: TERMS OF A FRACTION 5 


1. The two terms of a fraction are and 


2. Which term shows how many units the fraction contains ? 


8. Which term shows into how many parts the integral unit has 
been divided ? 


4. From which term do you get the name of the fractional unit ? 
5. Give the numerator and denominator and the use of each : — 
oy aay YL; ee eee 0-5 eee al, 


6. Name the fractional unit in each. How many of each make 
one integral unit ? 


7. How many kinds of units in $5,3,? In 34 ft.? 


8. An integer with a fraction added is called a number. 


DECIMAL FRACTIONS 


1. Compare 1 with 0.1; 0.1 with 0.01. 


2. In our decimal system of writing numbers how may we give to 
any figure a certain value and then a tenth of that value ? 


3. What effect upon the value of a figure has moving it one place 
to the right ? To the left ? 


4. What fractional units must fractions have before they can be 
expressed decimally ? 


5. How do you know the denominator, or size of the unit, in deci- 
mal fractions ? 


6. For what is the decimal point used ? 


7. Name the size of the units in each order, beginning at the first 
order at the right of ones, and reading to the right. 


6 REVIEW: READING DECIMALS Oral 


I. Read the following. WU. Give numerator and denominator. 
III. Give the value of each figure separately. 
oe 5. 4.053. 9. 0.1478. 
2. 0.54. 6. 0.765. 10. 16.47. 
ee AVE 7. 0.249, 11. 18.475. 
4. 0.003. 8. 0.319. 12. 9.0364. 


13. Which are mixed decimals ? 
14. Where is and used in reading decimals ? 


15. If you should express the above decimals as common frac- 
tions, how would the number of decimal places compare with the 
number of zeros in the denominator ? 


ABSTRACT AND CONCRETE NUMBERS 


LS tts (One Lih iL Oe oye ames. 
Which of these numbers are concrete, that is, associated with some- 
thing? Which are abstract, that 1s, which are used alone without 
reference to any particular thing ? 


2. Classify: $275; 362 1b.; 875; 1000; 600 acres; 90 men. 
3. What is the unit in each of these numbers ? 


4. Select those having like units, that is, those having units of 
the same kind and size. 


5. Tell what kind of number, and the unit of each: — 
A fts. B 25k ya.y (O05 18s) 10.865 016 tts ard: 
6. Give the integral and the fractional unit in the following: — 
43 dozen; 214; 94 quarts; 2.1 seconds. 
7. Which of the following have the same integral unit: — 
t1b.; 40z.; $ton; 2000 1lb.; ton; 4 cwt. 
8. Change the unit without changing the value: — 
36in.; 6ft; 14 ft.; 120sec., thr; 4 wk. 


Oral REVIEW: UNITED STATES MONEY iT 


1. What is meant by a decimal system ? 


2. Why may 1.23 represent dollars, dimes, and cents and not 
yards, feet, and inches ? 


3. How many dimes represented in $12.625 ? 


4. How are dimes usually read? What does the 5 represent ? 
How is it usually read ? 


5. Read and explain the use of the zeros: $7.77; $7.07; $7.7; 
$7.70. Does $7.7 differ in value from $7.70? 


fiead the following, (1) as dollars, cents, and mills; (2) as dollars 
and cents; (3) as dollars and thousandths : — 


6. $38.19. 10. $0.625. 14. $6425. 

7. $5,192, 11. $ 309.083. 15. $290 222, 
8. $24,072, 12. $ 400.040. 16. $80,025.95. 
9. $36,051. 13. $ 64.375. 17. $8005.025. 


18. Write the preceding numbers from dictation. 
19. Express as dollars and cents and mills : — 

$2h;  $20yy; $4; $24); $52; B64, 
20. Name four silver coins. What is a nickel ? 
21. What other metal is coined ? Into coins of what value ? 
22. Whatisaneagle? A double eagle? A quarter eagle? 
23. Whatisa mint? What is bullion? 
24. Are mills ever coined ? Of what use are they ? 
25. What is counterfeit money ? | 
26. What gives value to paper money ? 


27. Are United States coins made of pure silver or of pure gold ? 
Why is an alloy used ? 


28. Find what is meant by 18-carat gold. 


1. 


REVIEW : 


Give the sum of 7 and 8. 
how could you find it by counting ? 


ADDITION 


At Sight 


If you had not learned this sum, 


2. Find and explain a quick way of adding the following: — 


lnonwairkoa 
lao kRaor 


lm wo aoNwkOa 


lo rmoRHae 


3 17 
83 
36 
64 
32 
68 

95 


lomak ie 


Explain what change you make before adding : — 
3 wk. and 14 da. 


3. 


Principle. 


2 gal. + 6 pt. 


7. Tyr. +96 mo. 
8. 
9 


2 ay 2s 
Ae gaan 


OT ts eu Osrins 


= —— pt.; 


4. dyd., 7 ft. and 24 in. 
5. In Exercise 4, why not change the 3 yd. and 7 ft. to inches ? 


Before unlike units can be combined into one sum their 
units must be made alike. 


6. 


48 oz. -- 2 lb. = —— Ib. 

tg t+t=7 

6 yd. + 36 in. = in. 
t+3= 19 


Practice until you can give the sum of these numbers instantly : — 


10. 
ke 
12. 
13. 
14. 
1857 
16. 
1B fe 
LS. 


46, 34. 
19, 71. 
53, 47. 
86, 32. 
38, 69. 
AT, 46. 
65, 25. 
32, 99. 
72, 88. 


19: 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 


127, 123. 28 
900, 140. 29 
560, 240. 30 
767, 232. 31 
808, 191. 32 
346, 509. 33 
888, 212. 34 
694, 106. 35 
333, 766. 


. 8000, 1798, 2000. 

. 1300, 2000, 175. 

. 4080, 1507, 6000. 

. 85, 300, 9000. 

+ ts Ts a5 a: 
10.0670: 1870.24: 

. 25%, 8%, 30%. 

. 0.41, 0.19, 0.40. 

. $4.75, $3.25, $7.87 


Written 


REVIEW: ADDITION 


Give directions for five steps in adding : — 


I. Arranging the numbers. 378 

II. Beginning to add. A92 

III. Setting down the sum. 864 

PV. i Carrying: 798 

V. Checking. 956 

3483 
Without copying, first add vertically ; then horizon- 

tally : — 
if 2. 3. 4. 5. 

6. $3.47 $14.69 $193.67 $4769.83 $6483.47 
7 $62 48.96 846.84 4892.16 8432.97 
8. 946 387.81 932.71 8487.66 6432.98 
9. 658 47.94 683.77 6989.84 8469.32 
10. 7.89 82.66 765.75 4829.41 9396.48 
11. 9.88 68.48 392.50 6832.47 9375.58 
12. Find the sum of the five sums of the columns. 


13. Find the sum of the six sums of the lines. 


. Why should these two sums be equal ? 


Add and check by adding upwards and down- 
wards : — 


15. 


$475.21 
649.85 
837.64 
246.89 
937.48 
742.37 


—_———— 


16. 


17. 


$ 648.93 
973.26 
387.92 
814.78 
687.34 
968.47 


$ 719.63 
854.56 
784.97 
469.38 
847.86 
952.78 


18. 


$ 963.94 
738.42 
697.18 
346.32 
923.76 
768.93 


——_—— 


19. 


$ 679.83 
759.94 
678.90 
543.21 
783.94 
989.76 


A 


679,458 a 
340,276 b 
950,673 ¢ 
268,479 d 
728,735 e 
629,876 f 
724,894 g 
548,975 h 
829,386 7 
445,876 j 
317,872 k 
763,874 _1 
689,983 m 
670,498 n 
988,875_0 
687,568 p 
994,693 gq 
849,376_7 
649,478 s 
384,925 t 
569,247 _u 
347,964 v 
976,394 w 
Fay 3 ko EGS Be 
917,966 y 
2997 G2. 


20. Make fre- 
quent use of 
Col Aa tor 
practice in 
rapid add- 
ing. 


10 REVIEW: SUBTRACTION Oral 


1. 8 from 17 leaves what? If you had forgotten, how would 
you have found out that 17 -8 =9? 


Make a problem in subtraction, using concrete numbers. 


Which is the swbtrahend, and which the minuend ? 


The three terms used in subtraction are ; , and 


The largest term 1s 


CF a 


How do you find the third term when you have the difference 
and ie subtrahend ? 


7. Howiis the third term found from the minuend and difference ? 


8. Which is the larger number, 3 ft. or 24 in.? Which is the 
larger quantity ? How can one be subtracted from the other ? 


9. A boulder weighs 7000 lbs., a stone block 4 ton. Find the 
difference in weight and explain the process. 


Where you can, give the difference, first like the minuend, then like 
the subtrahend, in the following : — 


10. 4 lbs. — 32 oz. = ——. 12. 10 hr. — 240 min. = ——. 
11. 60 mo. — 2 yr. = ——. 13. 2T.— 2 lb. = ——. 


Give in one minute or less the difference between each number and 
the one below it ; between each number and the one at the right of it. 


a LL OS AS eT AOS Le ed ee aL i ee ae ee 
aie) Tie op te: 6 Vb 8 4 Sap 
b DF 69 tO ALG vai tL La ea 6S Sl Aad os Ae Le ae (45 
Dam 0 Sho tel 6 arent ) 4 9 
c iRay A TULO HAD {Lae Oe ese Se 
i hiee 4 58 Ome aL Hi 5 4 a 
d DAU, 2) EG aaah a Ro heals Kini Maype bate) let ls de se 6 
8 4 ein he Pas, Tong O01 Be) 3. A 


Oral REVIEW: SUBTRACTION 11 


1. From 97 count backward rapidly by 6’s; 8’s; 9’s; 12’s, 
2. From 200 count backward rapidly by 15’s; by 12’s; by 22’s. 


3. Give the difference between 100 and each of the following: — 


a He OSs 144 er aa voce OelroOr lo OU Of jor 48. 1 Sl 8h 
b SO ROL NES Lalo 22.605 A253 18 O91 69° 47 
G: 80,2009 25 01 6892435) 95° 29») 68 $2 | 84°26) 79° 16 
d. DOSE TO ane cla Ob) GOYA 93 etl 66+) 58> Ol 
e Ole Oo meoavOr Lo s0- 40: 1076 249 1d, 62h 27 5 85 
if: BLT O40 28084) 89°) 78. 88. |-80 25 | 97 54. |.98 40 


4. Give the difference between each number and the one at its 


5. Give the difference between each number and the one below it. 
6. ‘From 1000, take 120, 175, 225, 350, .760, 807, - 901. 
”. Take each number in the table from 173. From 182. 


What change from a $ 5.00 bill in payment for :— 


8. Oysters, $0.75; 9. Gloves, $1.25; 10. Pens, $0.35; 
Crackers, 0.88; Scarf, 0.75; Ink, 0.15; 
Cheese, 0.62? Pin, 2.50 ? Paper, 0.88? 


Subtract at sight : — 
ji 0 12. ES 14. 15. 16. 


700 3000 60503 25000 35111 36459 
325 800 40402 37892 46221 47560 


Find what remains after receiving and paying as shown below : — 


RECEIVED PAID RECEIVED PAID RECEIVED PAID 
17. $1.16 $0.93 18. $45.00 §$ 28.00 199. 2.20 ato 
0.24 Q.17 95.00 19.00 O19 2.30 


0.60 0.25 70.00 23.00 1.25 1.25 


12 REVIEW: SUBTRACTION 


From 683 take 457. . 
1. If you try to subtract one order at a time, 
teharetagt 683 what is your first Serene bL 
Subtrahend, 457 Pa Ake you had 83 sticks in bundles of 10 each, 
Remainder, 226 with 3 sticks over, how would you subtract 7 
sticks ? 

3. How many bundles would remain? How many sticks over 
would remain ? 

4. You would then take 5 tens from what ? 


5. What terms may be added to check the work? 


PROCESS 


6. Give directions for each separate step in the process. 


Written Exercise for Drill 
Without copying, find quickly the sum of the four differences between : — 
1. eand 3.9 and h. 6... cand 7 ye iysa one on aie 
2. fandg. 4. handi. 6. jandk. 8. landm. 10. nande. 


A B C D 

ée. $ 3764.82 $ 4769.31 $ 5000.37 $ 9000.15 
i 927.35 3468.97 689.82 794.38 
9g 860.85 385.68 1348.75 1866.75 
h. 1527.96 2487.52 946. 2889.43 
i. 3784.98 694.39 37.89 648.95 
j. 2876.45 1748.64 9586.34 1864.37 
k 825.35 4839.87 829.85 624.94 
£ 96.47 658.34 1472.98 1739.41 
m 849.53 1987.62 468.52 866. 

n. 276.41 594.83 5500.31 49.75 


11. Calling A and B the two sides of an account, find the balance. 
12. Do the same with O and D. 13. With Band @. 
What will balance : — 
14. A and C. 


15. Dand A. 16. Band D. 


Oral REVIEW: ADDITION AND SUBTRACTION is) 


1. Four parts of 75 are 18, 9,13 and 22. Find the fifth part. 


2. 37 gallons are ina tank. While 28 gallons run out, 17 run in. 
How many gallons remain ? 


3. An engine goes forward 25 rd., back 388 rd., forward 60 rd. 
How far is it from the starting point ? 

4. How much farther is it around a 17-foot square than around a 
13-ft. square? How did you get your result ? 

5. By annexing to 57 the figure 6, how much is added ? 


6. Bought a pony and phaeton for $500. Sold the pony for 
$175, losing $50. What did the phaeton cost ? 


7. Having $400 in the bank, a person draws $25, deposits $150, 
draws $75 and $50. How much remains ? 


8. One horse is worth $50 more than a second and $150 more 
than a third. If the highest priced one is worth $200, what are 
they all worth ? 


9. If you get 5 eggs one day and 6 the next, how many dozen 
will you get at this rate in a week ? 
10. How far around a rectangle 15 feet long and 10 feet wide ? 
11. Around a rectangle 18 feet long and 12 feet wide? 


12. My book contains 170 pages. I have read 82 pages. How 
many more have I to read ? 


13. IT had $100 ina bank. At different times I drew out $ 12, 
$18, and $20. How much remained? 

14. A farmer had 75 sheep. He sold 45 and bought 17. How 
many did he then have ? 

15. A trader had 29 horses and bought 57. He then sold 69. 
How many had he left ? 


16. Ina farm of 160 acres, 23 was woodland, 47 pasture, and the 
remainder grain. How much in grain? 


14 REVIEW: ADDITION AND SUBTRACTION Written 


1. How much remained in bank to Mr. Rich’s credit Saturday 
night, if he put in and took out the following : — 
Deposits: $ 26.95, $793.82, $427.96, $ 839.64, $500, $387.28; 
Withdrawals: $18.56, $ 689.37, $419.28, $ 649.39, $ 600, $125.82? 


2. I have on hand at the opening of business, cash to the amount 
of $846.95. I pay out $84.92, $64.87, and have on hand at night 
837.69. What have I received ? 


3. I received during the day $249.85, and I paid out $521.75. 
I had on hand at night $37.62. What had I on hand at the opening 
of business in the morning ? 


4. Thomas Bond begins business January 1, with cash $478.37 
and merchandise $1875.28. At the close of the year he has 
$1487.63 worth of merchandise and $738.29 in cash. How much 
has he gained or lost during the year ? 

5. The sum of two numbers is 346,301. The smaller is 89,795. 
What is the larger? © 


6. What number must be subtracted from one million to leave 
the difference between 347,698 and 486,931 ? 


7. The distance from A to B is 628 feet, from A to C 1426 feet, 
and from B to D 1648 feet, all in a straight line. How far is it from 
C to D? Draw a lne and mark off the distance. 


Find the excess of exports from this country when the exports and 
imports from 1898 to 1902 were as follows : — 


YEAR EXPORTS IMPORTS 
8. 1898 $ 1,255,546,266 - - $634,964,448 
9. 1899 1,275,467,971 798,967,410 
10. 1900 1,477,946,113 820,140,714 
11. 1901 1,405,375,860 880,419,910 
12. 1902 1,360,696,355 696,270,009 


13. Find the increase or decrease of imports and of exports from 
year to year. 


Oral CASH ACCOUNTS 15 


1. A debtor is one who owes another, or is in debt to another. A 
debit is something owed. 


2. A creditor is one to whom another owes a debt. A credit is 
an amount owed to one’s account. 


38. An account with “Cash” is, as it were, an account with one’s 
pocket book or cash box. Cash is debtor, that is, owes me, for all 
that is put in, and cash is credited with all that is taken out. 


DT CASH Cir 
1903 1905 

Apr. 1| On hand $100 | 00 May 3] By Mdse. bought || $450 | 00 
5| To Rent received 50 | 00 4| By Piano bought 350 | 00 
7| To Mdse. sold 25 | 00 8} By Clothing bought 25 | 00 
10} To Land 725 | 00 11] By Balance 75 | 00 

900 | 00. 

May 22] On hand 75 | 00 


4. Cash is charged with having received four amounts, which it 
owes me, that is, for which it is my debtor. How much on hand at 
the beginning ? 


5. What is the total amount Cash has received, that is, it owes 
me or 1s debtor for how much ? 


6. When I take out $350 with which to purchase a piano, Cash 
has paid me back how much of what it owes me ? 


7. What other amounts has Cash paid me, that is, for what other 
amounts should Cash be credited ? 


8. How much more has Cash received than paid out ? 


9. How much more might I have spent so as to balance the 
footings ? é 


10. For what is Cash debtor at the beginning of the next 
account ? 


16 


1. Balance the Cash account of Charles Watson. 
He receives at various times $6.24, $7.36, $8.49, $7.34, 


$4.21. 


BALANCING ACCOUNTS 


$6.75. He pays out $8.75, $9.81, $8.39. 


Written 


He has on hand 


2. Monday morning a merchant begins business with $247.84 on 
hand. He receives $24.75, $86.91, $84.28, $97.25, $164.29. He 


pays out $18.99, $37.49, $64.91, $83.15. 


hand. 


Find the balance of each of the following accounts : — 


aT: 
$ 987.65 
1859.76 
6482.91 
478.85 


698.47 


Dr. 
$ 246.94 
839.76 
842.94 
327.68 
946.32 


Dr. 
$ 94.68 
37.95 
469.38 
24.38 
6.49 
17.32 


Cr. 
$629.55 
83.74 
968.71 
28.46 
318.93 


Cr. 
$ 839.75 
646.81 
794.32 
546.78 
937.89 


Cr: 
$ 986.84 
69.39 
74.29 
83.62 
45.39 
169.38 


4. 

Dr. Cr. 
$4768.82 $468.34 
947.61 984.59 
847.77 1483.22 

3998.64 
8372.91 
ake 

Dr. Cr. 
$698.32 $649.83 
316.59 478.88 
843.26 694.31 
695.98 883.24 
831.96 695.64. 

10. 

Bye Cr. 
$346.85 $249.65 
976.87 998.54. 
695.79 648.36 
949.83 799.35 
697.87 869.40 
749.78 309.79 


Dr. 
$ 649.81 
8439.87 
648.38 
91.76 


Dr. 
$ 356.78 
938.12 
45.23 
938.85 


876.23 


$192.48 
765.35 
362.93 
15.56 
746.29 


126.48 


Find the balance on 


Cr. 
$135.72 
873.54 
137.92 
7639.85 
736.29 


11. 


$129.76 
947.34 
274.56 
1286.54 
364.92 
3647.10 


Oral REVIEW: MULTIPLICATION 17 


1. In combining unequal numbers, as 9+8+7+4= 28, what 
is the process called ? 


2. T4+7+747 or 4X7T=28. What is each of these two 
processes called ? 


3. Could the unequal numbers, addends, in Exercise 1, have been 
combined by a shorter process, as in Exercise 2 ? 


4. If you do not know the product of 5 x 8 from memory, how 
may you find it? Which number is to be multiphed? Which is 
the multiplier ? 


5. What does the multiplier show? Then can it ever be a 
concrete number, as 5 men, 5 feet, or 5 strokes ? 


6. Compare addition and multiplication. 
7. What are the three terms in multiplication ? 
Since the multiplier and multiplicand make the product, they 
are called factors (makers) of the product. 


Name quickly the factors, less than 14, that produce :— 


8. 65, 72, 77, 78. 11. 96, 99, 104, 108. 
9. 81, 84, 88, 91. 12. 110, 117, 121, 130. 
10. 48, 52, 54, 63. 13. 132, 143, 156, 169. 


One of the two equal factors that make a number is called the 
square root of the number. 4/ means “the square root of,” thus 


14. V64=-——; V8l=——; V121=——_; Re ae 

15. V9x25=3%x5 0r15; V16 x 25 =—_;; V25 x 86 =—_-; 
V25 x 49 = —_. 

16. V49x36=——_;_ V36x81=——_;_ V9 x 144=—_;; 
1/36 x 121 =——. 


17. V4x16 x 25=2x4x5 or 40; V4 x 25 x 86 =—_; 
V9 x 16 x 49 = —_. 


18 REVIEW: MULTIPLICATION Oral 


1, LSB S B39, fac esiggete i eG eae 
2. Give the factors, saying which is the multiplier and which 
the multiplicand: $42; 63 ft.; 72 yd.; 12 sq. ft. 


3. Make two examples; the multiplicand concrete in one and 
abstract in the other. 


4. What kind of a number was the product in each case? 
5. Can the multiplier be concrete? Why? 


6. Show by objects that 3 x 4 things of a kind are 12 of that 
same kind. 


7. Give the factors of $21; 35 miles; 18 cases; 49 men. 
8. Compare 4 x 5 bu. and 5 x 4 bu. 


Give each product quickly, stating which factor is multiplicand : — 


9. 10. a7 12. 13. 14. 15. 
$ 800 600 ‘700 rd. 900 800 da. 400 6000 
9 BUD ase: ene aby _16 men 13 


Prinocrptes. I. Only one factor can be concrete, both may be 
abstract. 
Il. The product and the concrete factor are like numbers. 
III. The order in which factors are used will not affect the product. 


Give rapidly the products : — 


16. 4x $8; 44 x $8; 3x 8%. 195° 3 <1 ORmddacr ee 
L713 Xp Os x beans OT. 20:u13ix 5 lee: 
18. 2x 3874; 5x124; 4x $14. 21°16 XA wy to: 


22. Multiply the following by 8; by 9; by 12: — 
7 bales, 70 bales, 80rods, 30miles, 90 feet. 
23. Multiply by 9 and add 9: — 
(Cam) orc Paras pee IB AY ees mI Ra Sibson mest (Ini wT EED 


24. How could you have got the same result in a shorter way ? 


Oral REVIEW: MULTIPLICATION 18 


1. Give two factors making : — 
G2 i 2) 40° T008 yO) eet; 1/78 3) 756 days; ) 81 men: 
2. Give two factors of 132 sec.; 125 in.; 144¢; 108 hr. 


3. Take 4x 7 from 9X 7. Howcan you do this without finding 
the products of 4x 7 and 9x7? 


4. From 9 x 8 take 6 x 8 in the same way. 
Se Lakemoogo trom 22 x9 16x 7 trom 2ux f, 


6. Add 18 x13 to2x13. To do this did you need to know the 
product of 18 x13? 


7. Add 17 x 25 to 13 x 25 in the same way. 


hae 


9. Add at sight 37 x 25 to 3 x 265. 


8. ox 6in. +7 xX 6 in. = 


10. From 63 x 8 take 13 x 8. 


11. 3*means 3 x 3) or 9; 5? means 5% 5 or 25. Find 4*; 67; 77; 
me Lerten BO 20 eOOs, 7 


erin 40-2 0e O00 = O07, 


13. Compare 5 and 50. Tell how you would multiply a number 
by 10. 


14. Compare 5 and 500. Tell how you would multiply a number 
_ by 100. 


15. How would you multiply by 1000, 10,000, etc. ? 


16. Multiply the following by 10, 100 and 1000: — 
59, 28, 147, 261, O15, 140. 


Principle. Hvery zero annexed to an integer multiplies it by 10. 


17. Compare 20 x 5 and 2x10 5; 507 with 5.x 10 x 7. 


REVIEW: MULTIPLICATION Written 

1. Under A what are added to get the B Ga 
result ? 489 489 
2. Explain the position of each product raid ae 
3423 34230 


and its real value. 


3. Show how the same result was got under B without 
setting down the partial products. 


4. Compare the work under B and C, and tell how to multiply 
by any number of 10’s, 100’s, ete. 


Find quickly the product : — 


Deo ATO, 9. 80 x 34,965. 185 80 KZ eo 
6. 8 x 4931. 10. 70 x 12,089. 14. 70 x 95,364. 
7. 9x 6989. 11. 300 x $42,794 15. 34,000 x 91,000. 
Sen COUS IL. 12, 30. X11203,900: 16. 28,000 x 75,000. 
Process Multiplying by any Integer 
ae 1. In the work at the left read the multi- 


3468=6 x 578. 


plier. 


23,120 =40 x 578. 2. What three partial products are used ? 
173400’ = 300 573. 3. Explain how each is obtained. 


199,989 = 346 x 578. 4. Would the result have been changed if 
we had multiplied by 300 first? By 40 first? 


5. In ordinary work what is omitted from each partial product ? 


6. Where is the lowest figure of each partial product written if 
the zero is omitted ? 


Give directions for six steps in multiplying : — 


1. Arranging the factors. 4. Arranging partial products. 


2. Beginning to multiply. 5. Finding the entire product. 


3. Setting downandcarrying. 6. Checking the work. 


Written 


REVIEW: MULTIPLICATION yaa be 


1. What is the cost of 2378 bbl. flour at $7 ? 


$7 multiplied by 
2378 must equal 


$ 16646 


2. Which is the true multiplicand ? 


for 2378 
multiplied by G 
equals 16646 


To shorten the work, why 


must we use abstract numbers as shown at the right ? 


Find the product of: — 


536 and 846. 8. 
3976 and 597. 9. 
37 ¢ and 482. 10. 
427 and 83 lb. 1 at 
329 and 347. ie 


Find the cost of:— 


iS: 
19. 
20. 
21. 
22. 
23. 
24. 


25. 
26. 
27. 
28. 
29. 


1579 bbl. sugar @ $9.87. 


6496 A. of land @ $34.89. 


12,865 T. of coal @ $ 4.87. 
16,492 lb. cotton (@ $0.09. 
24,975 lb. wool @ $0.35. 

6425 cords wood (@ $6.98. 


47,000 ft. lumber @ $42.25 
per M. (per 1000 ft.). 


5600 bu. wheat (@ $0.89. 
2745 bbl. cement (@ $1.25. 
47,892 gal. oil @ $0.08. 
135 bbl. pork @ $16.87. 
2892 kgs. nails (@ $3.09. 


Gog andro (6s wis. 
$627 and 931. 14. 
36 doz.and 453. 15. 
864 and $45. 16. 
387 and $8. 


30. 
. 42,000 lb. coffee @ $ 0.23. 
. 6425 pairs shoes @ $ 2.25. 
. 176,000 bricks @ $12.84 


84 qt. and 96. 
346 and 19 ¢. 
8477 and 86. 

98 oz. and 43. 
17. 304 posts and 97. 


7859 bu. potatoes (a) $ 0.79. 


Pele 


. 45,761 ft. granite @ $0.75. 
. 43,628 sq. ft. land @ $0.29. 
. O79 T. ice @ $4.67. 

. 47,000 shingles (@ $3 per M. 
. 87 gal. alcohol @ $2.65. 

. 375 bu. corn @ $0.87. 

. 3784 lb. butter @ $0.22. 

. 967 doz. eggs @ $ 0.18. 


42. How many rods in 54,000 miles ? 


43. How many square inches in 937 square feet ? 


44, How many seconds in 18 days ? 


92 MULTIPLICATION; ANALYSIS; STATEMENT OF PROBLEMS 


Oral and Written 
Give at sight :— 


1. 17x$94+3x$9=2. 4, 125x$9.85—25 x $9.85=2. 
2. 87x $7.504+13x$7.50=a. 5. 987x$125+63 x $125=2. 
3. 64x $48+36 x $48=2. 6. 157x316 ft.—57 x 316 ft.=2. 


Use. the same method in finding : — 
7. 649 x $12.84 less 145 x $12.84. 
8. 317 x $19.83 + 524 x $19.83 + 160 x $19.83. 
9. 975 x 846 4+ 973 x 352 — 973 x 198. 


Analysis and Statement of Problems 


Much work may be saved in solving problems if a statement is 
made showing all that is to be done to get the result before any 
figuring is done. 


1. Which is easier to do; to reason about a problem so as to 
show how it may be solved, or to figure out the result after being 
told how to solve it? 2. From which do you learn more ? 


3. A statement of all that is to be done to get the result written 
as equal to something denoted (for convenience) by the letter 2, 
is called an equation. Make a problem in which the equation 
4 x 161¢ =a will indicate the work to be done. 


4. $2.50 was the expressage on 19 tables at $12.74, and 28 chairs 
at $2.58; « was the total cost. 


STATEMENT. $2.50 + 19 x $12.74 + 28 x $2.58 = & (or the total cost). 


Make an equation showing all that is to be done to find the value 
of x; then find it: — 

5. 130 men at $2 a day, 47 at $1, and 8 at $3.50 receive 2 
dollars in one day. 


6. A nursery contains 1000 trees; 75 are dead ; Oe rest are to be 
sold at $2 each. They will bring $a. 


Oral REVIEW: DIVISION 23 


Finding an Unknown Factor 


.1. The product of two numbers is 48. One is 6. Find the 
other. 

2. How many 9’s in 54? What number is contained 9 times in 
63? In 108? 
Ses fo u5) the multiplicand; how many times is it taken to make 

the product 84 ? 

4. What multiplicand, repeated 12 times, makes the product 108 ? 

5. When one factor and the product are known, how is the other 
factor found ? 

6. Illustrate by using « xX $6=$42; and5 x $a7= $45. 

7. Why is the process called division ? 


8. Show by the examples in Ex. 6 that: — 
(a) The product becomes the dividend (something to be 
divided). 
(b) The known factor becomes the divisor. 
(c) The unknown factor, when found, becomes the quotient. 


(d) The quotient shows either, how many times the divisor can 
be taken out of the dividend, or the size of each of the 
equal parts into which the dividend is separated. 


Give the quotients : — 


9. 15x «= 30 days. 12. 12x %=144 miles. 
10. «x $9 = $108. 13. «x 9 ft. = 1385 ft. 
Lie Oe a= 120, T4eeo, xtliivd. Sad oleyd: 


15. Give the quotients in the following : — 
6)120; 96+ 24=%. 360=%; 72: 4=2. 
a 18 
16. Describe the four ways of indicating division shown in the pre- 
ceding line. 
17. Find any two factors :—96 bbl.; 91 days; 168 hr. ; 182¢. 


24 DIVISION: PRINCIPLES Oral 


1. How many $10 bills make $300? If one factor of 60 yd. 
is 10 yd., what is the other ? 


2. In multiplying two factors to make a product, which factor 
is always abstract? Which may be concrete ? 


3. In division, which term corresponds to the product? Which 
to the factors ? 


4. Can both dividend and divisor be concrete ? 


5. Show by the first example on the page that if the dividend is 
concrete and the divisor like the dividend, the quotient is abstract. 


6. If 8 hats cost $40, what will 1 cost ? 


7. A rod 90 inches long was cut into 10 equal parts. How long 
was each part ? 


8. Show by the above example that if the dividend is concrete, 
and the divisor abstract, the quotient shows the size of the equal 
parts into which the dividend has been divided. 


Principles. I. A divisor that is like the dividend is one of its equal 
parts and the quotient shows the number of these parts. 

II. An abstract divisor of a concrete dividend shows into how many 
equal parts the dividend is to be divided and the quotient shows the size 
of one of these parts. 


9. When 20 books cost $40, what part of it will one cost ? 


10. One factor is 15. The product is 90 yards. What is the 
other factor ? 


11. The divisor is 12, the dividend is 108 bushels; what is the 
quotient ? . 


12. The divisor is 9 ft., the quotient is 11; find the dividend. 
13. The dividend is 2100 mi., the divisor 21 mi. ; find the quotient. 
14. At17¢ a yard, how many yards can be bought for $1.53 ? 


Oral REVIEW: THE PROCESS OF DIVISION 25 
1. Division is the reverse of 
and 72 +9= 8. 


2. If you had not known that 8 xX 9=72, how might you have 
found the number of 9’s in 72? 


; since 8 x9=72,72+8=—9 


3. Find by subtraction the number of 12’s in 60; of 24’s in 96. 
4. How many 12’s in 1740 ? 


5. Are there 200 12’s in 1740? A 
Ve 12)1740 
oe Are there 100? ‘Subtract them ; what 1200 = 100 12’ 
remains ? 540 
7. How many 12’sin 540? Are there 50 ? 480 = 40 12’s 
Are there 40 ? 60 ; 
8. Subtract 40 12’s; what remains? Ueda es 
Total = 145 12’s 


9. 60=how many 12’s? Subtract them; 
what remains ? 


10. How many 12’s in all have been taken from 1740 by the three 
. subtractions ? 


11. In practice what part of the work might be omitted ? Where 
may 1 be written to show by its position that it stands for 100? 
Where may 4 be written to show it stands for 40? 


In practice the work is written as in the margin. a 145 
12. Short Division. Perform aloud the work of C. 12)1740 
How does short division differ from long division ? 1 
13. If 3465 is divided by 58, in what place me 
Z ) 48 
12)1740 should the first quotient figure be written { a 
145 14. 3465+19. How many figures in the 60 


quotient ? 
15. When should short division be used ? 
16. How may division be tested or checked ? 


17. How may the process of multiplication be proved correct ? 


26 


Pe WO WO EH 


EXERCISE IN DIVISION Written 


How many 15’s in 4650 ? 

27 XxX —— = 40,527. 

Dividend = 9672; divisor = 372; quotient = ——. 

96 and 75 are factors of what dividend ? 

Product = 33,810; one factor = 245; «=the other. 

One factor of $475,000 is $250; what is the other ? 

84 equal numbers make 6500 yards. Find one of them. 


360 miles = multiphcand; 25,520 miles = product; «= multi- 


. Divisor = $250; dividend = $16,750; «= quotient. 

. The divisor =197; the quotient = $461; the dividend = 2. 

. I received $1394 for 17 horses. What was the average price ? 
. Divide $39,624 into 48 equal parts. 


. Find J, of 3627. 15. Divide 3962 by 49. 
. Find 7, of 39,627. 16. In38962 ounces, how many pounds? ' 


. Divide $82.36 into 32 equal parts. 


Find the quotients : — 


18. 
19. 
20. 
21. 
22. 
23. 
24. 
39. 


759,470 + 78. 25. 89,175 + 39. 32. 183,974 +94. 
624,798 + 48. 26. 284,603 -+- 98. ' $8. 265,371 + 88. 
182,347 -- 57. 27. 99,134 + 49. 34. 104,288 + 78. 
96,343 + 97. 28. 108,264 - 57. 35. 139,267 + 72. 
(192,462 ~~ 67. 29. 346,271 + 86. 36. 204,306 + 68. 
236,475 + 77. 30. 937,441 +163. 37. 307,961 + 96. 
187,931 + 68. 31. 784,267 + 269. 38. 198,001 + 67. 
Divide each number in Column A, page 9, by the divisor formed 


by the last 3 figures in the dividend used. Thus: 679,458 + 458. 


Oral, Written SHORT PROCESS IN MULTIPLICATION 27 


1, Compare 5 with 4,2. Compare 5 x 84 with 12 x 84. 
2. What does 42 x 84 mean ? cs ; 84 _ what fi 


3. Describe a short method of multiplying by 5. 
4. Compare 25 with 192. Find 25 x 84 by a short method. 
Multiply each of the following by 5 and by 25: — 
ig EE eres AKO 9. 35. 11. 208. Ted92s7 1B. 49: 
Gr JOS Gun S.6e | i LOASZ¢: 12/,°308: 14.1695. 16. 63. 
17. By what must 124 be multiplied to make 100 ? 
18. Compare 124 with 19° Multiply 96 by 124 by a short 
method. 
19. By what must you multiply 162 to get 100? {of100 =? 
20. Compare 162 with 129. Multiply 42 by 163. 
21. 40f100 is what? 331=192, Multiply 45 by 33}. 
Multiply the following by 124, 162, and 333: — 


22. 48. 26. 405. 30. 114. 34, 295. 
23. 96. ithe P4se $1. 207. 85. 349. 
24. 72. 28. 64. 32. 345, 36. 642. 
25. 108. 29. 93. 33. 216. 37. 784. 


38. 1of 1000= what? Give a short method of multiplying by 
125. 

39. Multiply by 125: 168; 256; 976; 856; 1040; 375. 

40-55% 64-8 x 6=—13°%)6. Why? 

41. 13x 6+418 x 4= what? 

42. Find 17 x 18 + 23 x 18+ 60 x 18 by a short method, 

Find the products : — 

43. 25x64. 46. 16x121. 49. 125x912. 52. 163 x 1026. 

44. 5x82. 47. 162x144. 50. 121x128. 53. 333 x 126. 

45. 14x25. 48. 25 x 256. 51. 25 x488. 54. 84 x 33}. 


28 SHORT PROCESSES IN DIVISION Oral, Written 


1. Compare the quotients of 24 + 2 and 24 + 6. 
2. Compare 380 + 10 and 380 + 5. 


3. If 38 is the quotient of some number divided by 10, 2 x 38 is 
the quotient of the same number divided by what ? 


4. Explain: 320+5=2 x 320+ 10 = 64. 

5. How do you divide a number by 10? 

6. Give a short method of dividing by 5. 

7. Compare 375 + 25 with 4 x 375 + 100. 

8. Explain: 925+ 25=4 x 925 + 100 = 3700 + 100 = 37. 
In the same way divide the following by 25:— 


9: 1325: 12. 1675. 15. 9675. 
10m SOLO: 13974525, 16. 10,275. 
Lili vo: 14. 17,875. 17. 9625. 


18. 96 +162 =? x 96 + 100. 
19. Give a rule for dividing by 162. 
20. Make a rule for dividing by 334. 


Use these rules in finding quotients in the following : — 


21. 2500 + 121. 25. $15 + $ 0.124. 29. 1675 + 25. 
22. 6400 + 33h. 26. $24 + $ 0.25. 30. 1925 + 25. 
23. 1300 + 334. 27. $36 + $ 0.162. 31. 8250 -~ 50. 
24. 1850 + 162. 28. $42 + $0.50. 32. 1750 + 162. 


33. How many will $3 buy at $ 0.25 each ? 
34. How many yards will $5 buy at 162 cents a yard? © 


35. I paid $8 for tea at 33} cents a pound. How many pounds 
did I buy ? 

36. My milk bill was $8.75 at 25 cents per gallon. How many 
gal. ? 


Oral THE USE OF SIGNS | 29 


() asin (8+4)x5=85,0or asin3+4 x 5=85, shows that 
the numbers inclosed or beneath are to be treated as one number. 

1. 9+6)x 8—5) =a; 84+7x10—5=«. | 

2.3xP4+7=0;4x10+50=a; 27+38—-V4=2. 

8. bb —-5 x2=e) 18-8225 =e; 10—4)+6—3=2. 
Observe the following and tell which process is performed first when 

xX or + is on one side of a number and + or — on the other : — 

4. 344x5=3420=28. 6. 6x12—8+2=72—4=68. 

5. 44-16-38 4-2 2—0: T 6x150+24+6=754+4=79. 

8. Compare in value 138 —5 X 2+8 and 13—5) x (2+ 8). 

9. 86+4—45+9=a%. 11. tof 7 +14) —tof 867—9)=2. 
10. 2+5x648+2=¢a. 12. tof 41—16)++2 of d9—T)=2. 
13. What expressions are here marked to be treated as one number ? 

8x 16+848x 16—9)=V3x9x3 x 108+12—10+1. 
14. What is the value of V64+4+8x2? 
15. (V100xX4—5) +5432, “18: (29+46—1) x 18=-2. 
16. (8?+6) x5+3+45=@. 19. (89+10)x2+6=2a. 
17. 4—-4x38+4+10—-—2x5=2. 20. (6?+4—10) x84+9=2. 
21. What number is to be divided by 11? 

(6x54+4x9)+11=[(6+5) x 00 —4)]+11. 

22. Show why it was better to use brackets [ ] than curves ( ). 
23. x” = (12?-+ 24) x V54—5. 
24. (4800 + 100) + 0.01 of 600 =a. 
25. w=[6x8—4 x (14—4) +60] = 100. 


26. (a) ve] n. 27. (12x446 x 12) +V100=2. 


28. x=[(7+3) x2—4 of 39). 
29. [(V25)?—V6 xt] 4:4 of 72—2. 


30 EQUATIONS Oral 


a —=12+25 means that w stands for some number which is equal 
to the sum of 12 + 25, hence x = 37. 


Find the value of x in the following : — 


1. we=12+ 25. 6. 42—¢=—19. 11. 19+-11+-4=—50. 
2. 88+12 =>. 7 «+17 =32. 12. 72+2+414= 96. 
3. 44—19 =~. 8. 28+2=50. 13. 40+ 20—2=50. 
4. e=100—72. 9. $—w=3. 14. $2.75 += $4.50. 
5. «—24=48. 10. llb.—w=12 02.15. «—$7.30=92.54. 


16. Lam 2 years old; in 8 years my age will be 36 years. 
(w+ 8 years = 36 years.) 
17. After taking $14, $16, and $12 out of a sum of money $3.75 
remained. There were $2 at first. «— $14 — $16 — $12 = $3.75. 


18. A prize cup contains 23 oz. of gold, 10 oz. of silver, and 2 oz. 
of alloy. The cup weighs 42 oz. (Make an equation.) 


19. 25 gallons run into a tank, and 46 run out. When the faucets 
were closed, 80 gallons remained. There were «# gallons in the tank 
when the faucets were opened. (EHquations.) 


20. Make a problem about the weather in March to suit this 
equation: 31 da. =12 da.+ a da. +10 da. 


3a means 3x. 3e=15 means that 3 times some number equals 15. 
Find the value of x in the following and explain your method : — 


1. 4x2=60. 6. 87=400. 11. 


| 
oo 


16. 4¢+-5=21. 


WO PIS 
bo 


2. 17xd5=—2. 7%. Te=91. 12. =4, 17. 1772—4=80. 


oe 7 of «=16. 8. 1472=700. Loy 


| 
ee 
Or 


18) 18% x10 = 180. 


4. 80+a=4. 91/25 0=6275. 914.--=4, 19. 42¢+21=70. 


le 8/S ble &8| 


5. 144+a¢=16. 10. 44”7=45. 15. —=7. 20. 4 of 16%=120. 


bo 
aN 


Oral, Written STATEMENT OF PROBLEMS 31 


1. If 16 cords of wood cost $120, 24 cords will cost what? In 
solving such a problem, which of these suggestions seem most 
important ? 

I. What is to be found out? (Cost of 24 cords.) 
Il. What facts will help to find this ? (16 cords cost $120.) 

Ill. Comparison of what is given to what is wanted. (24 cords 
will cost 14 times as much as 16 cords.) 

IV. Process, briefly set down. (14 x $120 = cost of 24 cords.) 

V. Work performed. (14 x $120 = $120 + $60 = $180.) 


VI. Does the result seem reasonable ? 


2. Bought 12 lb. tea at 75¢, and 20 lb. coffee at 40¢. How much 
butter at 30¢ would cost the same ? 


12 x $0.75 + 20 x $0.40 _ 
$0.30 Ctr 

3. Exchanged a 60-acre farm worth $ 2400 for 200 acres of wood- 
land valued at $18.75 an acre. Find the gain. 

STaTEMENT. 200 x $13.75 — $2400 = x. 

4. Gave 3000 sq. ft. of 20% land for a span of horses and $75. 
What were the horses valued at ? 

Statement. 38000 x $0.20 —$75=~-2. 

5. A man purchased 130 bbl. of flour at $4.50 per barrel, and a 
number of barrels at $4. He paid $665. How many barrels of 
the cheaper flour did he buy ? 
$665 — 130 x $4.50 __,, 

$4 es 

6. Sixty-four men are employed 25 days in digging a sewer. The 
contract price was $1200. Nothing was gained or lost. What were 
the men paid each per day ? 


7. If 14 lb. cost $2.94, what will 10 lb. cost ? 
8. If 17 tons of coal cost $134, what will 51 tons cost ? 


STATEMENT. 


STATEMENT. 


32 MISCELLANEOUS PROBLEMS Written 


Applying the suggestions on the preceding page, state the following 
and explain orally :— 


1. I bought a field of 10 acres for $1000. I sold 7 acres of it at 
$125 an acre, and the remainder at $85 an acre. How much did I 
gain ? 

2. I sold 50 acres of land for $5000. This was a loss of $15 
per acre. What did the land cost me? 


3. A boat goes 10 miles an hour -downstream and 6 miles an 
hour upstream. How long does it take to go 30 miles and return ? 


4. If 15 men can do a piece of work in 90 days, how long will it 
take 6 men ? 


5. If 14 bbl. of apples are worth $35, what are 21 bbl. worth ? 


6. A train runs 280 miles in 11 hours. Seven 3-minute stops 
are made, and a hot axle makes a detention of 39 minutes. The 
rate per hour was 2 miles. 


7. Six men buy 640 acres at $125, and sell for $95,000. Each 
man gains w + of ($95,000 — 640 x $125) = each man’s gain. In 
the statement what represents the cost of the land? The proceeds 
of the sale? The whole gain ? 


8. Bought 39 bbl. of flour at $4.75; sold 15 bbl. at $5, and the 
remainder at $5.25. Required, my gain. 


9. Three 1-pound packages will go by mail each for 1% an ounce 
plus registration; by express, for 25¢ each. Which way is cheaper? 
10. A peck, 2 bushels, and 5 quarts are to be divided equally 


among 7 persons. Any two receive x quarts. 


11. I spent $4485 for cattle and horses, buying the same number 
of each. If I paid $75 apiece for the horses, and $40 each for the 
cows, how many of each did I buy ? 


SucexrstTion. What did 1 horse and 1 cow cost? Then how many times can 
I buy a horse and a cow with $4485 ? 


Oral and Written MULTIPLYING BY MIXED NUMBERS 33 


1. Explain the process in each of the following: — 
Do Xd ia K Lo ey OE 2 So. 
2. Give the results of the following: — 
34x 8; 85 x 10; 54 x 15. 
3. What does 2 of 9mean? Find 2 of 9; 3 of 16; 3 of 10. 


Nore. The sign of multiplication (x) may be used instead of the word ‘‘ of” 
but it must always be read ‘‘of’’ and not ‘‘ times’’ when the multiplier is a 


fraction. Thus, 
3 x10 means 2 of 10. 


4. Give results: — 2x 20; 4x 28; 2x 45; % x 56. 

5. Give results:— 8x72; 3x 63; 2 x 36; $x 40. 

6. 0.05 of 20 means 4 of 20 or 5 x 1 of 20. 

7. zy or 0.1 of 20=—; 1, or 0.1 of 50 = —; 0.1 of 45= 
8 


10 


. Give results : — 0.6 of 20; 0.8 of 60; 0.9 x 70; 0.08 x 400. 
9. 25 % =25 or 0. —; 6% =0.—_; 6% of 200 = —. 
10. 8% of 400; 15% of 400; 16% of 500; 17 % of 1000. 
11. Compare 3} with 10. Show a quick way of multiplying by 33, 
12. Compare 831 with 100 and show a quick way of multiplying 
by 33. 


13. Give results: — 


34x15; 34x18; 334 x 24; 334 x 36. 576 
14. Supply omissions in the multiplication 8% . 
_at the right. 82 x 576. 12 =% of 576 
ee 504 = 4 of 576 
15. Give directions for each step in multi- AG08 — . 
plying by a mixed number. 5112 = 81 ¥ 
Written Work 
16. 93 x 280. 19. 780 x 193%. 22. 13,3, x 280. 
17. 183 x 942. 20. 603,35 x 2000. 23. 148 ft. x 784. 


18. 11055 x 144. 21. 18% x 1728. 24. 911 lb. x 1080. 


34 MISCELLANEOUS EXERCISES Written 


1. If the Empire State express runs 115 miles in 108 minutes, 
what is the rate per hour ? 


2. If 71 cu. ft. of water weigh 2 tons, how much will 2414 cu. 
ft. of water weigh ? 


3. I paid $59.22 for potatoes, and sold them for $70.56. What 
was the gain per bushel, if I paid 94 ¢? 


4. My July gas bill was $5.28 for 4400 feet of gas. In August | 
the gas company raised the price +. How much should my August 
bill have been, if 1500 feet of gas were consumed ? 


5. At the end of August the reading of the meter was 5600. At 
the end of September the reading was 7400. What is my gas bill 
for September at $1.25 per 1000 cubic feet ? 


6. The mailing clerk in the office of the Herald receives $10.95 
for mailing 52,850 papers weekly. How much is that per hundred 
papers ? 


7. The Transvaal gold output in August, 1899, was 459,700 oz., 
and its value was $9,194,000. The August output in 1902 was 
valued at only $3,200,000. How many ounces were mined ? 


g. Find the amount of a bill for the following: — 


28% yd. silk @ $1.80. 
24 yd. percale @ 0.121. 
2% yd. velvet @ 2.25. 

8 yd. silk @ 2.90. 


9. A merchant purchased 950 barrels of flour at $6.90. He sold 
325 of these at $7.20, 460 at $8.10, and the remainder at $9. 
What was his total gain ? 


10. A fruit dealer bought 500 oranges at the rate of 2 for 3¢, and 
400 more at the rate of 4 for 5¢. He sold the whole lot at the rate 
3 for 5¢. What was his gain ? : 


Oral COMPARISON OF NUMBERS 35 


1. If 5 lb. of cheese cost 80 cents, 10 lb. will cost what ? 
2. Why is it needless to find the cost of 1 lb. in Ex. 1? 
3. At the rate in Ex. 1, what will 23 Ib. cost? 

4. When 21 lb. of steak cost $3.21, what will 7 lb. cost ? 


5. Compare the time required by 6 men to do a piece of work 
with the time required by 2 men. By 12 men. 


6. Compare the rent for 5 mo. with the rent for a year. 


7. If a house rents for $500 per year, what is the rent for 5 
months ? 


8. 5 bushels of oats cost $1.70. At this rate, what will 15 
bushels cost ? 385 bushels ? 


9. 9 for $1 makes 6 cost what? 12 will cost what ? 
10. $386 is what part of $108? Of $72? Of $144? 


11. What 42 men can do in a week will take 7 men how long? 
How long will it take 28 men ? 


12. Supplies that will maintain a regiment of 1000 for a week 
will maintain 100 how long? 600 men how long? 


13. If 6 men can do a piece of work in 10 days, how long will it 
take 4 men to de it? 


14. If 8 men can build a wall in 3 weeks, how many men will be 
required to build it in 1 week ? 


15. If 60 horses eat 450 bushels of oats in a month, how long will 
it last 80? How long will it last 90? 


16. If 12 dozen eggs are worth $1.80, what are 8 dozen worth at 
the same rate? What are 60 dozen worth? 


17. If oranges sell at 3 for 10 cents, what is that a dozen ? 


18. 4 ounces for 25 cents is how much per pound ? 


36 PROBLEMS Written 


1. Compare the cost of 36 bu. with the cost of 12 bu. The ratio 
of 36 to 12 is 


2. If 12 bu. cost $7.50, what will 36 bu. cost ? 

Compare the cost of 85 yd. with the cost of 17 yd. 

If 17 yd. of cloth cost 18.70, what will 85 yd. cost ? 
Compare the cost of 114 gal. with the cost of 19 gal. 
1) gal. of alcohol cost $72, find the cost of 114 gal. 


Oo oT Fe & 


ie Compare the time required for 91 men to do a piece of work 
with the time required for 15 men. 


8. If 13 men can pave a street in 42 days, how long will it take 
91 men to do it? 


9. What will 364 bbl. of apples cost when 52 bbl. cost $175 ? 


10. What is the relation (ratio) of ali of anything to 20% of it? 
When 20% of a crop of beans is 325 bushels, what is the whole 
crop ? 

11. What is the relation (ratio) of all of anything to 162% of it ? 
If 162% of a certain number is 342, what is the number ? 


12. A barrel of flour fills 8 bags and costs $4.50. What is the 
gain on 3 bbl. sold at $0.621 per bag ? 


13. If Hans can haul as much sand in 15 days as Knut can haul 
in 20 days, which should receive the higher wages ? 


14. If Knut receives $60 per 20 days, what should Hans receive 
per day ? 


15. What is the ratio of all of anything to 50% of it? If 50% of 
a certain distance is 168 miles, what is the whole distance ? What 
is 25% of the distance ? 


16. Compare 9000 lb. with a ton. What should I pay for 9000 Ib. 
of hay at $12.50 per ton ? 


Written DENOMINATE NUMBERS 37 


Change 
1. 3 da. 6 hr. to hours. 12. 13 T. 1600 lb. to pounds. 
2. 18 hr. 43 min. to minutes. 13. 9 bu. 8 qt. to quarts. 
3. 6 yd. 17. in. to inches: 14. 11 yd. 24 in. to inches. 
AS sds tt. LOT sq. cin. to 15. 9 hr. 48 min. to minutes. 
square inches. 16.75 ¢u. ft. 15635" cu. in.’ to 
5. 8 cu. yd. 16 cu. ft. to cubic cubic inches. 
feet. 17. 356 qt. to gallons. 
6. 5 gal. 3 pt. to pints. 18. 150 oz. to pounds. 
7. 3 mi. 240 rd. to rods. 19. 17,562 cu.ft. to cubic yards. 
8. 5 bu. 8 pk. to quarts. 20. 34,628 sec. to hours. 
9. 2wk.5 da. 11 hr. to hours. 21. 348 wk. to years. 
10. 9 A. 120 sq. rd. to square 22. 1965 qt. to bushels. 
rods. 23. 3468 cu. ft. to cubic yards. 
11. 9 lb. 3 oz. to ounces. 24. 3462 gi. to gallons. 


25. Change 120,000 min. to days. 

26. Thirteen tons of oatmeal will make how many one-pound 
packages ? 

27. How many pint bottles can be filled from 728 gallons of ex- 
tract ? 

28. A team of strong horses haul 5 tons of granite. How many 
cubic feet in the load if each cubic foot weighed 165 pounds ? 

29. Bought 3 acres of land and cut it into house lots, each con- 
taining 3267 square feet. How many lots were there ? 

30. How many rails 60 feet long will be required to lay 20 miles 
of double track railroad ? 

31. How many 3-ounce packages can be made from a quarter of a 
ton of pepper ? 


32. How many pint bottles of mineral water can be filled from a 
tank holding 300 gallons of mineral water ? 


38 COMPARISON; RATIO Oral 


1. 24=2x 12; 12=1 of 24. 


What is the difference between two ways of comparing 24 and 12 ? 


In this way compare the following numbers : — 


pee Ie chivas 5. 20 and 80. 8. 49 and 7. 
3. 15 and 60. 6. 25 and 125. 9. 63 and 9. 
4. 25 and 75. 7. 30 and 90. 10. 42 and 6. 


11. Compare 3 in. and 2 ft. ; 2 yd. and 6 in. 
12. What is the relation of 3to9? Of4tol6? Of 5 to15? 
The relation of one number to another is their ratio. Ratio is ex- 


pressed as the quotient of the first number divided by the second. Thus 
the ratio of 6 to 2=3; of 2 to6=4. 


13. Read these five ways of expressing ratio: — 
The ratio of 12 to 24is 4; 12:24=4; 12+24=4; #2=1; 12 
is to 24 as 1 is to 2. 


14. What is the ratio of 12 to 60? Of 124 to 100? Of 15 to 45? 


What is the ratio of :— 
15. 121 to 25? 18. 81 to 162? 21. 20to 30? 


16. 16 to 48? 19. 61 to 25? 22. 60to 90? - 
17. 162 to 50? 20. 374 to 75? 23. 108 to 144? 


24. What is the ratio of 121 to 183 ? 


SUGGESTION. 121 is 2 6}’s, and 183 is 8 63’s, hence the ratio is 2 to 3, or 2. 


What is the ratio of : — 

25. 121 to 314? 28. 61 to 25? 31. 162 to 414? 

26. 121 to 75? 29. 84 to 162? 32. 3314 to 2662 ? 
. 27. 374 to 874? 30. 162 to 100 ? 33. 662 to 300? 


REVIEW: PROBLEMS FOR ANALYSIS 39 


If 15 oranges cost 40 cents, 5 will cost what part of 40 cents ? 
If 3 cost 7 cents, what will 15 cost ? 

If 64 lb. of honey cost 95 cents, what will 25 lb. cost ? 

Give two equal factors of 3600, that is, 3600 = what ? 
Divide 21,000 by 3000. Explain your method. 

Find the value of ¢ of 2400 — 3 of 1500. 

Find the sum of 3600 + 120, 3, of 2400, and ;4, of 75,000. 


900 


V121; V81; 144; 400; 1600; V/2500. 


3X 0x T7+5xX6= what? What common factor in both 


friend and divisor may be dropped ? 


10. 
Uae 
12. 


men. 


13. 
days ? 


14. 


Divide 4 x 6 x 8 by 6; by 8; by 4; by 24. 
How many 7’s from 910 leave 700 ? 


Compare the work done by 9 men with the work done by 15 
Compare the time required by them to do a piece of work. 


How long will it take 15 men to do what 9 men can do in 10 


At the rate of 8 for 9 cents, what will a dozen cost? What 


will 24 cost ? 


15. 
16. 
VE 
18. 


2 ounces for 40 cents is how much per pound ? 

40 sq. rd. of land for $1000 is how much per acre ? 

If 6 inches of pipe cost 35%, what will 1 yard cost ? 

If 18 pounds of sugar is worth $1.00, what will a bag con- 


taining 63 lb. be worth ? 


19. 


20. 
1000. 


Divide 360,000 by 4000; 90,000 by 4500. 
Divide 3600 by 100; by 1000. Divide 280,000 by 100; by 


40 DENOMINATE NUMBERS Written 


1. Bought 44 barrels of flour at $51 and sold it in 1-bbl. bags at 
70¢. Find my total profit. 


2. When lessons are $30 per quarter, what is the average cost 
per week ? 

3. How many days in a leap year? How many weeks and days 
are there ? 

4. Bought an 8-peck barrel of cranberries for $8 and retailed 
them at 2 qt. for $0.25. What was my profit ? 


5. A bushel of wheat weighs 60 lb. What is a ton of wheat 
worth at 86 cents per bushel ? 


6. At 60 1b. to a bushel, 3 bushels to the barrel, 9 tons of beans 
will fill how many barrels ? 


7. Bought a field 600 ft. long and 413 ft. wide. What will it 
cost me to fence it at $1.25 per rod ? 


8. A man travels 23 miles per day on every day except Monday, 
when he goes 6 miles farther, after resting on Sunday. How many 
weeks will it take him to go 576 miles ? 


9. Bought 130 tons of coal by long ton (2240 lb.) at $4.00 per 
ton, and sold it by short ton (2000 lb.) at $6.50 per ton. How much 
did I make on the lot ? 


10. I paid $300 for an acre of land and sold it for 25¢ per square 
foot. How much did I gain or lose ? 


11. Give the length of a double track railroad laid with 1056 rails 
30 ft. long. 


12. Ocean steamers sometimes use 300 T. of coal every 24 hours. 
This is how many pounds per minute ? 


13. The velocity of light is 186,337 miles per second. - Light from 
the sun reaches the earth in 8.3 minutes. What is the sun’s mean 
distance from us ? 


TESTS FOR DIVISIBILITY 45 


1. Any number is a multiple of 2 if the last digit is zero or a 
multiple of 2, that is, if it ends in 0, 2, 4, 6, or 8. 


2. Any number is a multiple of 3 if the sum of the digits is a 
multiple of 3. 


For example, 3 will divide 1278 for it will divide 1+24+7+8 
or 18. 


3. Any number is a multiple of 4 if the last two figures are zeros or 
express a number divisible by 4. 


Thus 38,236 is divisible by 4 for 36 is. 
4. Any number is a multiple of 5 if it ends in 5 or 0. 


5. Any number is a multiple of 6 if the last digit is even and the 
sum of the digits is divisible by 8. 


6. Any number is a multiple of 9 if the sum of the digits is. 


Thus 327,654 will contain 9 for 34+24+7+6+5+44 or 27 will 
contain 9. 


7. Any number is a multiple of 10 if it ends in a zero. 


8-14. Which of these numbers are multiples of 2? Of3? Of4? 
GOO 7a O19 te OF 107 


360. 6984. 2160 3654 3741 
1728 8397 3240 1782 1746 
3123 6624 9270 4662 8460 


Making use of these tests to find the common factors, change the 
following to largest units : — 


15. 6/428 = 3/21 = Jt. 22. 198, 26. 282. 
16. 342, 19. 198, 23. 216, 27. AL. 
17. 349. 20. 225. 24, 279, 28. 252. 
18. 315, 21, 248, 25. 495, 29, 125. 


46 ADDITION AND SUBTRACTION OF FRACTIONS Oral 


What are ike numbers? Give examples. 
What isaninteger ? Name some integers and the unit of each. | 
Whatisafraction ? Name some fractions and the unit of each. 


Show the difference between an integral and a fractional unit. 


o FPF WW DO 


In the folowing numbers name (a) the integral unit, (0) the 
size and kind of fractional unit, (c) the number of fractional units : — 
5 pk.; 75 yr-3 ps3 BS; Zin.; $0.15; 6% of a day. 

6. Which of the following fractions have units of the same size ? 
Of the same kind? Of the same kind and size? . Which are like 
fractions ? 
éYT5 FIT Hs Fda; $F; pyd; § mi 
7. Why not add ¢ lb. and $4? #2 wk. and 4wk.? 


Principle. before fractions can be added (or their difference found) 
their units must be of the same kind and size, that is, the fractions must 
be like fractions. 


8. tet fe tit = ae 11. 35 — $e = ot 
Ble Sek. OIE ae C 12. 72% —zty=0.48, 
10. 0.55 =26 == 01308 13. 162+4+183= 


14. 14 da.+ 3 wk. = 
make before adding ? 


da.. or 


wk. What change did you 


15. Mention some unlike fractions. Why are they ‘unlike ? 


16. 4,3,4,2. Which of these fractions have a common numerator ? 
A common denominator ? Which are like fractions? Which are 
unlike ? 

17. 6 +2+2475+44+43=2. (Add the like fractions first.) 

18. 34+ R= Can 12 be changed to 6ths? Why will it be 
better to veo L to 6ths rather than + to 18ths ? 

19. In Exercise 14, why would it be on to change the 14 days 
to weeks ? 

20. 2+4%=a. Why change 3 to 24ths? 


Oral and Written ADDITION AND SUBTRACTION OF FRACTIONS 47 


1. Which term is common to like fractions ? 


9 


2. Change 2 and 58, to like fractions, or a common denominator. 


oO 


Change to the least common denominator (L. C. D.). 


.8. In adding 3 and 4% shall we use 4ths or 60ths as the com- 
mon unit? Will 4 or 60 be the least common denominator ? 


4. Why is it easier to use the largest common unit (or the least 
common denominator) in adding ? 


5. Give three steps in adding 7 and §. 


Method. In adding or subtracting unlike fractions. 


I. Change to a common unit. 
Il. Add numerators or find their difference. 
Ill. Simplify the result. 


Perform the operation indicated in the following : — 


By eset ees 9. $422. pee 
To 4 38. 10. 3+3 13. 24%+4 
8. ish i. $4 Me +h 
LASS rele: aoa wy anion om a 20. ¢t+ayetet+etsa 
160 20 + 1 020 + 4, 21, $4184 25491 
17. 2841444104 259, SOU USB UNE te Oude 
18. $+ yy +39 +46 2. H—$+h+4 
19. 18% +.0.12--4 + 2. pte Salle Li'l URS eA Ta 


25. +wk.+ 52, yr. +i da.—- mo. + 180 min. = 2. 


Multiples; Common Multiples; Loast Common Multiples. 
Show that 36, 60, 72 and 120 are multiples of 12. 
Show that 50, 60, 80, and 120 are multiples of 10. 
Show that 60 and 120 are common multiples of 10 and 12. 
Show that 60 is the least common multiple (L. C. M.) of 10 and 12. 


Pm Oo WwW 


48 LEAST COMMON MULTIPLE Oral and Written 


1. Find the least common multiple of 30 and 42, t.e. a multiple 
containing only such factors as are needed to produce each number 
separately. 


WorK 
a Le): 
AZ AGO OG 


42 x 5 = 210, the least common multiple (L. C. M.). 


ExpLANnATion. A multiple of 30 must contain all the prime factors of 30, 
and a multiple of 42 all the prime factors of 42. Now, a number whose factors 
are 2, 8,5, and 7 will contain 2 x 3 x 5, or 30, and also 2 x 8 x 7, or 42. In 
practical work we say 380 x 7, or 42 x 5, since 7 is not found in 30, or 5 in 42. 


2. Find the L. C.M., i.e. the least number divisible by 60, 72, and 108. 


Work 
60=2x2x3x 5. 
(22 X20 Xo ro. 
108 == 252 x oe OOS. 
LOS 26 5 == 080 the: iG M3 
(a) What prime factor of 60, needed in the L. C. M., is not found 
in 108 ? 
(6) What prime factor of 72 is not found in 108, that is, found 
more times in 72 than 108 ? 
(c) What is meant by the least common multiple of several 
numbers ? 


3. Find the L.C. M. of 60, 84, and 132. 
4. What is the least common multiple of 45, 90, 100, 200 ? 


Sueerstion. Isa multiple of 90 a multiple of 45 ? 
Is a multiple of 200 a multiple of 100 ? 
Notice that we need simply to find the L. C. M. of 90 and 200. 


Find the L. C. M. of :— 
5. 15, 21, 45. 6.1116; 18227, 72: 7. 16, 25, 80, 100. 


Written FRACTIONS: ADDITION AND SUBTRACTION 


1. Add 44 and 54. 
PROCESS 
Le 
1S ='3'x Bx 2: 
18 x 5=90, the L.C.M. 


49 


EXPLANATION. Since the common fractional unit could not be readily seen, 


we found the L. C, M. of the denominators. 


2. Js+y =o. 7. G++ =2 

3. + ise 8. fot t +ib=e 
4.ctit=" + 9 ge +4$t+it=a. 

5. tHe 10. §} +t =e. 

ey taias 11. H+ H+ Hae | UTS 
Pood eoore 74s Ge sis) Add 


and this result to the sum of the integers. 


13. Add 325, 1714, 24,7,, 364 and 212. 


15? 
14. From 75,4 take 5744 


PROCESS EXPLANATION. 


90ths, then, is the largest common 
unit to which both 15ths and 18ths ean be changed. 


(Reduce each to larger 


Why ?) 


the fractions mentally 


or 42 from 75 and add to the fraction #$. 


Since the fraction in the minuend 


How is this 


tt is smaller than the one in the subtrahend, we take 1 
(= 


S741 = nate = 5 
ns = 178 


19. 14,9,—6.51, 


21. 
22. 
23. 
24. 


734 — 1614. 


71d — 1948. 
8423 1585, 
17145 —91.8,. 
4815 — 1347 


like ‘subtraction of integers when a figure in the sub- 
trahend is larger than the one above in the minuend ? 


20. 


25. 114441612 + 8419 — 1633. Can you find some short way 


of doing this-without changing a fractions to a common unit? 


50 FRACTIONS: MULTIPLICATION Oral 


I. To multiply a fraction by increasing the number of units. 


1. 9x7 units = units. 


2. In Exercise 1, does it matter whether the units are integral or 
fractional ? 


3. Then it follows that 9 x 7 eighths = 63 eighths ; 9 x 7 = 43 


AL ene lan ee 10. 16x 2. 
54 Cie toe ae” Vieille 
GoM ss 9. 15x34. 12. 10x 4. 


13. In the preceding exercises did we change the number or the 
size of the units ? 


Il. Yo multiply a fraction by increasing the size of the units. 


1. Compare }and1; and 4; + and 5. 


Oune mal 7 
2. Compare 3 and 33; 2 and 3,; 7 and 5%. 


16> 
3. How does dividing the denominator affect the size of the 


units ? 


4. Compare 3 days and 3 weeks. What is the unit in each? 
Why is 3 weeks 7 times as large as 3 days? 


5. AX in ‘. What change in the value of the fraction when 
i 


we take { instead of .? Why? 


Find the product by increasing the size of the units : — 


6. 6X 45. 9. 10x 55. 12. 15x 45. 
7. 8x28. 10. 12 x 42. 13. 25 x +158). 
8. 3x HH. 11. 18x 3. 14. 36 x 43. 


Principle. A fraction is multiplied by any number either by mul- 
tiplying its numerator or dividing its denominator by the number. 


« 


Oral and Written FRACTIONS: MULTIPLICATION 51 


The multiplier a fraction ; the multiplicand an integer. 
How can you get 9 x 7 by addition ? 
What does the multiplier show ? 


3. Is it proper to say 4 times $6? That is, can $6 be taken 1 
of a time as an addend ? 


4. In finding + of $6 to be $2, do we multiply or divide ? 


on! 


While such expressions as 2 X $9 are called multiplication, the $9 
has not really been multiplied, that is, increased. 

When preceded by a fraction the sign x must be read “of.” The 
expression means 3 of $9, that is, 2 times one of the 3 equal parts of 
$9, or 2 x $3. 


5. 3 x 24 hr.=3 x G of 24 hr.) or 3X3 hr. or 9 hr. In practice 
3 
we say ; Neel Chigpet a4 NH 
Se aah eal bh 10. § x 20. 14. 438 x 105. 
Tae Xo 11. 5% x 50. 15. 47 x 144. 
8. 14 x 84. 120030 100. 16. 47 x 226. 
9. = x 60. 13. 33 x 100. 17. 4% x 840. 


II. One factor a mixed number. 
18. At $0.95 a pound what will 


PROCESS 
& 0.95 742 pounds of tea cost ? 
TAL 19. 182 cords of wood at $8.75? 


9)$6.65 =7 x$0.95 20. 15 yards at $0.18? 
18 
9 


Wes oh rie 21. 278 yards at $6.25? 
coll ES AM 
BOO ee TON 0.05 22. 73 months’ rent at $28? 


$ 71.038 = 747 x $0.95 23. 32 tons at $8.75? 


When the final result includes 24. 93 bushels at $3.40? 


; ve 
a fraction of + cent or more, it is 25. 400 dozen at $ 0.162? 
customary to count the fraction 


as another cent, 26. 125 feet at $0.347 ? 


52 PROBLEMS IN FRACTIONS - Written 


1. 4,2,and 4+of a number=110. Is the unknown number larger 
or smaller ? Hon do you know ? 


2. A barrel is 2 full. Draw off 4 of a barrel and 2 of a barrel. 
What part remains ? 


3. A stone wall cost $1 a rod. What costs 3 days’ work, or 
62 rd., 53 rd., and 72 rd. ? 


4. A chimney contains 132 courses of brick. 4 are under ground, 
24 roofed in; how many courses are exposed ? 


5. How BED cords of wood in 2§ cd. sawed by hand, 4 ed. by 
machine, and ;% cd. chopped ? 


6. Two pumps contribute 4 and 4 toward filling a reservoir, 
springs contribute 4 and i, surface’ water the rest. How much 


more do the pumps yield than other sources ? 


7. Inan11-acre marsh lot three men cut 4, 5%, and 2 of the whole. 
What part remains for a fourth man to cut? How ies acres ? 


8. If you invest ;2; of what you have in one way and 3 in another, 
what remains ? 


9. At $3 a day what is due a man for working half a day, 2 da., 
$da., and 214 da. ? 


10. What remains of a 49-yard piece of cloth after selling of it, 
2 of the rest, and 4 yards? What is the remnant worth at 85¢ per 
yard ? 


11. Another piece of 47 yards is damaged. One half sold at 7¢. 
Of the other half 23 yards were unsalable, but the rest went at 5 ¢. 
Give the total receipts. 


12. At the rate of $13 a day, figure a board bill in dollars and 
cents for 3 months from August 1. 


13. Ifa glacier moves uniformly a hundred feet a year, how far 
does it go in 181 days? 


Oral and Written FRACTIONS 53 


Finding the Fractional Part of a Fraction 


1. 2 of 6 things (apples, collars, fourths) = x things. 
2. 2 of 10 twelfths = x twelfths; 2 of 18 = 4 ori. 
3. 2 of 12 5. 8 of 27. 7. 73; of 82 
4. 7 of 18 6. 3% of 42 8 1 of 


To multiply 2 by 2 is to find 2 of 2: that is, to divide 3 into 5 equal 
parts and find the value of 5 of these parts. 

9. How does increasing the denominator affect the size of the 
fractional unit ? 

10. If we take a denominator 5 times as large, how is the size of 
the fraction changed ? 

11. Then fof }=4. If{ ofa fraction = 5%, 3 of the same frac- 
tion will be how many times 3, ? 

12. Make arule for finding the product of two fractions, i.e. for 
finding one or more of the equal parts of a fraction. 

13. Find 19 x 24. 


PROCESS 


10 24 10x24 240 4 (a) Of what use is cancellation? 
12 “ 35 12x35 420 7 (0) On what principle is it based ? 


Ste) (c) Which is easier, to change the 
ae 10 ¥ 74 _4 product to lowest terms or to cancel 
12 pp 7 first ? 
7 

14. 3% x #. 17. 23 x 2 20. fy X 23. 
15. 4 x $4. 18. 85% x +4 21. 5 x $3. 
16. 33 x 33, 19. 96% x #3 22. 44 x Pf. 
23. 83 x 68 = 32 x =a 
24. 2x Th 28. 4 of 3 of 34 32. 16% of 54 
25. 22 x 735. 29. 22 x 44 xX Tehq- 33. 84% of 355 
26. 4% x 153. 30. $x 14x f. 34. 72% of 32% 
27. 63 x 246 31. 12 x 54 x 1,545 35. 19% of 182 


54 FRACTIONS Sight Products 


Multiply each fraction in the table by the number at the end of its line 
or column. Change any fraction in the product to a smaller denomina- 
tion when possible. Thus: — 4x3 yd. = 2° yd.=22 yd.=2 yd. 8 in. 


12 4 6 10 15 
2 3 qt 3 yd. 3‘ hr. 7 sq. yd. 121% 12 
3 2 yd Z gal 41 da. 33; min. 162% 1 
4 5 pk 33; lb qe ft 41 sq. ft 334% 10 
5 2 ft. +5 yr. 43 T. ay Sec. 621% 9 
6 2 wk. 3% in 3 ed. zy hr. 374% 8 
fl 8 9 12 7 


Written Work. Problems 
Make out bills in full for : — 
) ibs es 

17 doz. at $ 1.624. 152 doz. 

173 yd. at 10¥. 13 yd. 

3. Find the cost of 92 tons of coal at $7.41. 

4. Twenty pounds of sugar bought at 4,%,¢ are sold for $1.25. 
At this rate what is gained on a barrel of 200 lb. ? 

5. Oil is bought at $3.50 for a 42-gal. barrel and retailed at 121. 
The gain is what part of the cost ? 

6. Oranges bought at 3 for 5¢ are sold at 4 for 9%. What is 
gained on a box of 9 doz., 1 in 12 of which are worthless ? 


7. I can buy blank books of one dealer at the rate of $1.25 a 
hundred; of another at $1.60 a gross. How much is one offer better 
than the other ? 

8. Find the cost of seven 50-gal. barrels of oil at three for $16.71. 

9. Supposing an empty barrel to be worth $1.25, what is the oil 
worth per gallon ? 


at $ 1.00. 
at 621¢. 


Oral DIVISION OF FRACTIONS 55 


I. When the divisor is an integer 
1. To divide ? into 5 equal parts, that is, ?+5=+4 of =~. 


CG 15 
2. enn are ies tana 
Observe that a fraction may be divided by a number either by divid- 
ing the numerator or by multiplying the denominator by that number. 


3. Observing Exercise 2, tell when you use one method and when 
the other, and why. Which is shorter ? 


4. 5 +7. 7. 4+12. 10. = + 6. 
5. 4+8. 8. 78 + 12. 11. 48% +16. 
6. 24-8. 9. 74 + 20. 12. 7335 +17. 


Il. When the divisor is a fraction 


13. 2ft.+38in.=«. (Since dividend and divisor must represent 
like units, we have 24 in. + 3 in.) © 


14. 3+2, Are the units of the same size ? 


rey 
a 
15. 3+2=9+35;9+8=14. 16. al ieee Cie 


17. What is the first step in dividing days by hours? Feet by 
inches? 4ths by 5ths? One fraction by another ? 


18. 2+ 2. 21. 75+. 24. 27+ 5, 
19. 14+ 3. 22. y+. 25. 18+ 3 
20. $+ 2. 23. +4. 26. ge+2 


27. How many 4thsin1? In2? Ind? 

28. How many 3dsin1? In4? In10? 

29. How many dthsin1? In10? In 20? 
30. 
31. 


| 
4 
= 
+ 
~ 
OO 
SS) 
= 

| 
~y 

I 


Ph pL bt 
| 
a ole ple 
I 
x) 
oo 
ASS 
jb 
| 
co|-  Oo|- 
| 
Secs es 
ey) 
~3 
fs 
| 
bol, 
S| 
| 


56 DIVISION OF FRACTIONS: THE DIVISOR INVERTED Oral 
8. l+i=-2@ 6 1 + 53. 9. 1 + 35. 


Notice that in each of the preceding exercises the quotient was 
the same as that obtained from dividing the denominator by the 


numerator. 
10. 
ied We 
12. 
13. 


Why was this ? 

Compare 6 + 2 and 12 + 2. 

What effect on the quotient if the dividend is increased ? 
How does 2+2 compare with 1+2? 

Compare 8 + 2 with 4 + 2. 


14. Compare ++ 2 with 1+ 2. 


We, Sees 


4 ys 
SuecEstion. Since 1 + 2 is 3, 3 + 2 is 3 of $ or 2 
ie ee ye aaeetods 
10. See 
EXPLANATION. Since 1 + 3 is 3, { + is 7 as great as 1 + 3, or is 7 of 8. 


17. The two methods compared : — 


First Mretuop Seconp MetTuHop 


(a) What advantage has the second method over the first ? 
(6) What disadvantage may it possibly have ? 


Notr. Cancellation may be used in division of fractions as in multiplication. 


Apply the shorter process and explain why it is shorter : — 


18. 2+ 3. 22. $+ 5. 26. 27+ 5. 
19. +4. 23. $+ 45. 27. ~p +. 
20. §+ 8%. 24. 34-3, 28. 0.32 + 18 
21. $§+41, 25. $+ 5. 29. 0.042 + 5%. 


Written FRACTIONS.: PROBLEMS 59 


1. An heir gets 4 of an estate, then loses 3 of his share. What 
part of the estate does he keep ? 


2. I buy at 20% discount. What is the total cost to me of goods 
sold regularly for $ 1.42, $ 3.98, $57, $ 0.162, and 9 pieces at $ 0.311? 


3. If 81 T. of coal cost $487, what is the cost of 68 T.? 


4, Property which cost $5000 is rented for $431 a month; what 
is the annual income to the owner after paying a tax of $15 ona 
thousand ? 


5. Three cheeses, weighing respectively 343, 423, and 474 lb., were 
sold for $ 20.60. What was the price per pound ? 


6. J. Ff. Sampson bought 721 bu. potatoes at 624 ¢ a bushel, and 
sold 2 at 642 g, the remainder at 75¢. What did he gain? 


7. An electric launch was sold for $ 285, or 42 of the cost. Find 
$2 of the cost, or the whole cost. Compare #2 with 32. 


2) 


8. 2 of a ton of hay at $ 20 pays for 14'T. of coal at how much a 
ton ? 

9. 161 ft. of 2-in. pipe at 64¢, and 1020 ft. of 1-in. pipe at 41¢, 
are exchanged for 120 lb. of tubing at 111f, and 134 ft. at 9%. What 
is the difference in value ? 


10. Two trains start together in the same direction. How far 
apart will they be in an hour if one goes a mile in 1,3, min. and the 
other in 85 sec.? . 


11. An express train runs 240 mi. in 54 hr. How far will it run 
in 3ihr.? (Compare 34 with 51.) 

12. A tank holds 168 gal. and is 2 full. 23 of the quantity is 
drawn off. How many gallons will fill the tank ? 


13. An automobile started at 10.45 a.m., and at 3.20 p.m. had cov- 
ered 641 mi. What was the rate per hour? 


60 FRACTIONS.: PROBLEMS Written 


1. A man had in a bank a certain sum of money. He withdrew 
2 of 2 of it, and gave his son 2 of 4% of that. What part of the 
whole amount did his son receive ? 


2. A man walked 29% mi. one day, and 213 mi. the next day. 
On the third he walked the difference between the two distances. 
How far did he walk in the three days ? 


3. A owned a farm as follows: 33% A. of wood land; 633 A. 
of meadow; 254 A. of good grass land; and 192% A. producing fruit. 
He sold 2 of the whole farm to a speculator. This was a A. 


4. If 3 bbl. of flour will supply 30 people 134 wk., how many 
barrels will it take to supply them 46 wk. ? 


5. A man traveled # of his journey the first month, and 2 the 
next month, when he found that he still had 660 mi. to go. How 
far had he traveled ? 


6. A boy bought 23 bu. grain and sold me ;4 of it. Another boy 
bought 3 bu. and sold me an amount equal to what I bought from 
the first boy. What fractional part of the second boy’s grain did I 

buy ? 


7. Bought 28'of a barrel of flour of one man, } bbl. of another, 
and +5 of the third. What was the cost at the rate of $6 a 
barrel ? 


8. I purchased 360 A. of land at $75 per acre, and sold $ of it 
at $85 per acre. After paying for the land, I had left # A. and §$ y. 


9. If 132 bu. of rice cost $11.75, what will 37% bu. cost? 


- 10. A man bought 100 yd. of carpeting, and sold 374 yd. to one 
man and + of the remainder to another. How many yards had he 
left ? 


11. How much larger is 24% + 7 than 24% x 7? 


Oral NUMBERS COMPARED: RATIO 61 


Compare with 100 :— 


1. 50, 25, 75, 20, 40, 10, 80,70. 2. 5, 15, 4,12, 16,2, 6, 8. 


Repeat rapidly until thoroughly learned 
parts of 100:— 


the values of the following 


cee ae be 8 St ge a eR iy ns A fe 0 ce oy Es ca 
en ko2 | OF. See? 02 50 SL Ote a2 lesen 02 O08 0 OF HL UO: 
Are TEI Be Le eS Bet ana Oe Oe aS ad 
teat G2 .62" 6! S262 5S 10), P23 216202 02925240 02) 7- 
§ 
(ie a koe 81) GUL IN Es Ma da an 9 3 pe DL NE be 
ee Uta aed O75 s 0%no D2. OU 129 16? 409 809 169 16° 
Gaye ee rg Tee pee Se OL 1 
p50 42.62.6773 7. 897 6: erg? 16) 1 2s 407 1G) 1 3° 


11. A nurseryman sells 2500 strawberry plants at $6 a hundred. 


They cost him 2 as much to raise, and he gives an agent 4 of the 
profit. How much does he gain ? 


Compare one number with the other in each of the following columns. 
Thus : — 


1. (a) The ratio of 8 to 24 is 4; (0) 8 is 4, or 334%, of 24. 


2. (a) The ratio of $ to 4 is 5 to 2, or 24; (6) 2 is 24 times, or 


250%, of 1. 
tt, 
8, 24 
60, 12 
24, 60 
48, 72 
162, 662 
#4 
375, 25 
1, 100 
2.75, 5.50 
1, 1000 


a 
iy 


89 4 
72, 60 
37}, 64 

6 

8 
5 2 
69 3 
10%, 20% 
$0.75, $ 1.25 
874, 874 


III. 
90, 18 
OZ Lal. 
2 gal., 3 qt. 


~ 30, 50 


4, 0.16 
0.68, 0.51 


| IV. 
1 da., 1 hr. 


1 wk.,1 da. 

5 min., 25 sec. 
144, 148 

rio aH 

4X yor 8 X oo 
0.93, 0.31 

200, 162 

$1, $1.50 

1.834, 1.00 


62 


NUMBERS COMPARED Oral 


Compare the following and give the ratio in per cent : — 


Thus, to compare 5 with 20, say 5 1s 25% of 20. 


i: 


2. 16 with 80, 6 with 42. 
3. 

4. 45 with 15, 48 with 36. 
5 


2 with 28, 15 with 40. 


. 385 with 105, 3 da. with 1 wk. 
. 4in. with 1 yd., 2 mo. with 1 yr. 


6 
f 

25 with 150, 24 with 42. 8. 1 oz. with 1 lb.,1 hr. with 1 min. 
9 


. 1 1b. with 1 0z., 100 lb. with 1 T. 
. 18 with 54,18 with 24. 10. 2 qt. with 4 gal., 1¢ with $1. 
Rib: 


What is the relation of the whole of anything to 2 of it, i.e. 
the relation of 2 to 2? 


12. If 12 is 2 of a number, what is the number? 


SUGGESTION. 


13. 


with 


2 
z* 


Since all, or 3, is 24 times 2, the whole number is —— x 12. 


If 28 is 2 of a number, what is the number? (Compare 3 


times as large ?) 


Is the number larger or smaller than 28? How many 


In this way find the whole when a part is given : — 


14. 
15. 
16. 
17. 
18. 
19. 
20. 
28. 
29. 
30. 


31; 


12 is 4 of what ? 21. 
16 is 4 of what ? 22. 
24 is 1 of what ? 23. 
19 is 2 of what? 24. 
28 is 2 of what ? 25. 
36 1s 2 of what ? 26. 
72 is 4 of what ? 27. 


100 is 42 of what ? 
450 is 43 of what ? 
175 is 25 of what? 
What part of 23 is 3? 
32 is 4 of what ? 

123 is 8 of what? 


142 is 2 of what ? 


What part of 2 is 33,? (Change to like units.) 
183 is what part of 621? (3 x 64 and 10 x 61.) 


A farmer sold 200 bu. of beans. This was 4 of his crop. How 
many had he? 


20, or 2 of a farmer’s sheep, are black. How many sheep 
has he? 


Oral NUMBERS COMPARED: PER CENT 63 


1. What does the phrase per cent mean? How many per cent in 
the whole of anything ? 


2. The sign % takes the place of what denominator ? 
3. What is the unit in 8% ? 
4. What is the ratio of all, or 100%, of anything to 50% of it? 
5. If 50% of a crop is 400 bu. what is the whole crop ? 
Find the whole when the specified part is known : — 
6. 16 is 4, or 50%, of what? 10. 56 is 4, or 874%, of what ? 
7. 241s 3, or 75%, of what? 11. 20 is 25% of what? 
8. 32 is 2, or 662%, of what? 12. 15 is 121% of what? 
9. 40 is 8, or 831%, of what? 13. 80 is 371% of what? 


PAVE eT is'10%) of == 17. V25 is 5% of —. 
15. 31 is 831% of —. 18. 36 is 18% of —. 
Tomer ist 20 peat ete 119, 9? is 27% of ——-. 


20. A teacher pays $6 per week for board and room. This is 
40% of her salary. What is her salary for a school year of 40 
weeks? (Her salary is how many times 40% of it?) 


21. A man’s expenses are $7.50 per week. This is 84% of his 
income. What is his income? (His whole income is how many 
times 81% of it ?) 

22. How much have I if $1.20 is 20% of my money ? 

23. Mary Smith’s salary is $750 per year. This is 331% of her 
father’s income. What does Mr. Smith receive annually ? 


24. After spending $5, James had 60% of his money remaining. 
How many per cent did he spend and how much had he at first ? 


25. I sold 60 of my flock of sheep. If this was 20% of my whole 
flock, how many had I left? 


Hint. How many per cent left? How many times 20% is the per cent left? 


64. PROBLEMS FOR ANALYSIS Oral 


EHzxplain exactly how you get each result : — 


10 = 12 of what number? 10 = 42 of what number? 

Give 4 and ;4, their least common denominators. 

# of a hill is dug away. How many times as much remain ? 
10+, =what? 10+ 4= what? 

A train goes a mile in12min. How far willit goin an hour? 
At 1 mi. in 90 sec., how much in an hour? 

50 mi. an hour = how much a minute ? 


At 48 mi. an hour, how long does it take to go 1 mi.? 


co aoant OO oT FF WO WD 


A mile in 124 i min. is the same as 60 mi. in 


10. 34% of certain telegraph lines are under ground. What per 
cent are above ground ? 


11. A foundry uses 100 T. of Swedish iron to 50 T. from other 
sources. What part or per cent of each class is used ? 

12. $160 was s&, or 16%, of the profits. What were the profits ? 

13. 23% of a certain stock was glassware, 69% was china. The 
rest was in brass goods, which were «% of the whole? 

14. The 5,000,000 sq. mi. of the Arctic Ocean are what per cent 
of the area of the Pacific, which is 16 times as large? 


15. I gain 100% on 4 my goods and sell the rest at cost. How 
much do I gain on $100 invested ? 


16. Ina36-column newspaper what part of the whole space would 
be filled by 20 columns of advertisements ? What per cent ? 


17. I lose half that I have, and 25% of the rest. What I keep is 
what part of what I lose ? 

18. The board of a horse is $ 20, shoeing $ 1.25, harness repairs 
$ 0.25, use of carriage $3, new whip $0.50. Each item is what part 
of the whole? Give per cents when you can. 


ADB es, OLD". 20. 2 = 2% of 87. 


Oral EXERCISES IN FRACTIONS 65 


1. Change to lowest terms 343; 74%. 
2. Compare results: 224.7 yd. +7; 224.4 yd.+7 yd. 
8. fof 1W=a. Zofl0=y. 

4, 5% league = what part of a league? 

5. 2A.=what partofi2A.? Of1,A.? 

6. 21s contained in +2 how many times? 

7. Cancel mentally: $ of § x 44 of #2 =a, 


8. By getting a uate of 2 I pay only $3.33. What is the 
regular price ? 
9. 478+ 5 =-%. 
10. What is the least that will pay for 1 article, when the price 
per dozen is — 


$1.05? $1.10? $1.15? $1.25? $1.30? $1.35? $140? $1.50? 
$1.75? $2.00? $2.25? $2.50? $2.75? $3.00? $5.00? 


11. 3rd. at $1.25. 13. 34 in 25 a times. 
12. 57% |b. at $1.28. Lae = 164 te a, 
15. kes + 874 4+.624 + 874 +1124 4121; 662 — 162 —81. 


16. By a Fahrenheit thermometer what is the temperature when 
the top of the mercury column is ;°; of the distance in degrees from 
zero to the freezing point ? 


17. After gaining ;5, or 10%, I have $99. What had I at first ? 
18. Find 21x90. Whatis 74, of it? 6% of it? 
19. What part of 100 is 94,? Give = of 100; #3 wb 


20. How much for a dozen at 16 for a quarter? At 4 for 5¢? 
At 20 for a quarter? At 3 for 10¢? At3 for 5¢? 


21. A newspaper weighing 4 0z. may be mailed for 1%. What will 
it cost to send — 


Llb.? 10 oz. ? 5 oz. ? Al oz. ? $ oz. ? 


66 | EXERCISES IN FRACTIONS Written 


1. Paid at different times 4, 4, and 54 of a debt. The balance 
was $1170.61. What was the whole debt ? 


2. 4 of an estate is divided equally among 14 persons, another 4 
among 9 persons. One of each of these shares is to be given to the 
heir of the remaining third. What part of the whole does he 
receive ? 

3. From a life-saving station to the end of the northern beat is 
2, mi. How many full steps will a surfman take in going and 
returning, if his steps average 2,2, ft. each ? 


4. The Minot’s Ledge light revolves twice a minute. It is 
lighted from sunset to sunrise. How many revolutions does it make 
between 5.52 p.m. and 5.52 a.m. ? 


5. Four equal farms, all adjoining, are offered for house lots. 
Parts of each are sold as follows: %, 5, 7%, 7%. Add the fractions 
and tell what the sum shows. 


6. What part of a mile is covered by 22 revolutions of a wheel 
18 ft. round ? 


7. Divide 231 cu. in. into 3 equal integral parts ; into 83. How 
else can it be exactly divided ? 


8. Just when does + of a common year end? + of a leap 
year ? 


9. A bushel of potatoes is commonly 60 lb. A thousand 56-lb. 
bushels are what part by weight of 1000 60-lb. bushels ? 


10. A barrel of 42 gal. will fill how many cans containing 
1% pt. ? 

8 

11. When $80 are earned in a month and 5, of it spent, the 


saving of 2,4, yr. at that rate would be how much ? 


12. A chest contained 74 lb. of tea at 55 ¢, 134 Ib. at 35 ¢, and 
98 lb. at 27 ¢, The mixture is worth wf? a pound, and $10 would 
buy y lb., with 2% remaining. 


Written FRACTIONS: BUSINESS TRANSACTIONS 67 


Find the cost of the following purchases : — 


1. 3h yd. silk at $1.374; 84 doz. buttons at 15¢; 74 sticks braid 
at 75%; 23 yd. ribbon at 162¢. 


2. 6470 ft. fencing at 9,5,¢; 3 lots land, 10,280, 7595, 8122 sq. ft. 
at 54¢; 3400 bricks at 8. 15 per M. 


3. 3450 Ib. coal at $8.25 a ton; 324 cu. ft. wood at $5.75 per . 
cord; 5460 lb. coke at $6.40 per tort 


4. Go over the computations in the following bill or invoice to 
find the errors it contains. 


Cuicaco, Aug. 1, 1904. 
Mr. Henry D. WARREN 


Bought of Joun V. FaARweitu & Co. 


May 18 | 23 yd. Brussels Carpeting @ $1.50 34 | 50 
June 22 | 161 yd. Black Silk @ 1.75 18 | 98 
July 6 | 388 yd. Wamsutta Cotton @ 0.123 4 | 75 
hale 23 
Less 35 82. 
41 
Cr. 
June 2 By Cash $ 25.00 
By Cash 20.00 —00- 
Received payment, 41 


JOHN V. FARWELL & Co., 
By Smith. 


5. Make out bill in proper form. Supply dates and names. 
13 tons Franklin coal at $ 7.25 


64 tons Lackawanna at 5.50 
1 Cord Hard Wood at 11.00 
31 bbl. Cement ee Ree 


68 FRACTIONS: BUSINESS TRANSACTIONS Written 


1. Friday, Jan. 1, 1904, Sam’l Chase had $32.76 to his credit in 
a bank. If he deposited $25 every week day during the month, and 
$100 extra every Saturday, what amount could he draw against 
HeboLa 


2. In buying 785 music books @ 85%, a discount of 1 or 20% is 
allowed on cash payments. The net cost is what ? 


3. Bill 62 lb. Formosa Oolong Tea @ 60¢ 
30 lb. Maracaibo Coffee @ 241 ¢ 
2 bbl. “ Bridal Veil” Flour @ $5.25 
Discount 2% [for cash]. 


4. Bill 374 yd. Dwight Cotton — (@11¢ 
421 yd. Scotch Gingham (@ 23¢ 
112 yd. India Silk (@ $1.75 
Credit mdse. returned, $8.75. 


5. Invoice 33 gro. No. 514 Eagle Pencils @ $4.20 
54 gro. No. 404 Gillott’s Pens (@ 0.374 
41 gro. 4to Blank Books (@ 3.66 


6. Colonel 8., a Kansas farmer, harvested 4000 acres of wheat in 
1903. He estimates the cost per acre as follows: for plowing, $1.00; 
for drilling, 25¢; for seed, 3 pecks to the acre at 60¢ a bushel; for 
heading and stacking, $1.25; for threshing, 20 bushels per acre at 
6¢; for hauling 4¢ a bushel. The wheat was sold at 60¢ a bushel, 
and the use of fields for grazing during the winter is worth $2500. 
Estimate the profits. 

Rule paper for an account that you keep with John Holmes. It 
will show that he is debtor for all that is sold to by and 


creditor for all that is paid to by as below. (See p. 15.) 
Joun Houimes Dr. Or. 
19— 3 
May 1 | To 8 Shares Mill Stock ‘} 812 | 00 


By 4 River Pasture (3 A.) |} 46° | 00 


Written BUSINESS TRANSACTIONS 69 


1. Complete Holmes’s account, found begun on page 68, from the 
following data: 34 days repairing Holmes’s fence at $2.50. Credit 
him for use of his oxen same time at $2. Sold him 23 bbl. apples 
at $1.40. Bought of him 3 hogs (732 Ib.) at 1119, and 11 tons hay 
at $15. Sold him 15 young maples at $1.061, and 3 hoops contain- 
ing 35 ft. strap iron at 23¢. Holmes paid cash $100. What does 
he now owe me? 


2. January 1 my gas meter read 67,500; March 31 it read 91,500. 
At $1.60 per thousand my quarter’s gas bill is $a. 


3. A week’s sales of wheat in bushels: 2137 , 0476, 972, 3041, 6782, 
1849. Valued at 623¢. What are the gross proceeds ? 


4. What did my house cost me as shown by these items : — 

Cellar, 18 days @ $14.75; mason’s contract, $4575.86 ; carpenter, 
137 days @ $2.15 and 96 at $3; materials, $576.84; painting, etc., 
$ 397.68 ? 

5. At an auction sale of land the following prices were obtained: 
3648 ft. at 237; 2894 at 314¢; 7642 at 194¢; 8641 at 25¢. The 
auctioneer’s Commission was o¢ on the dollar, and puvauuiatne; etc., 
cost $37.50. Required the net proceeds. 


6. Bought a 100-acre wood lot for $800. Paid 23 men $517.50 
for 18 days’ work at cutting. Sold 175 cords at $2.37, 215 at $4.25, 
and the remainder with the lot for $800. What did I gain? 


7. A farmer wintered 17 horses from December 1 to April 1 at 
$12amonth. He paid $23 a ton for 22 tons of hay, and 42 cents 
each for 280 bushels of oats. He had $14 worth of provender left. 
He made $a a month. 

8. I can buy of one firm 732 tons of coal at $4.20 and 75 cords of 
wood at $8.16. Another firm bids $4.16 for the coal and $8.35 for 
the wood. Shall I buy of the first or of the second, and save what ? 
. 9. There are 2741 operatives on a corporation. 12 overseers get 
$3.50 a day, 25 second hands get $2.50, 4305 earn $1.50, 215 men 
and 731 women earn $1.25 each, and the remainder on the average 
receive 96 cents. What is the weekly pay roll? 


70 FRACTIONAL MEASURES Written 


290 ft. hemlock boards at 13 ¢ will cost how much ? 

3.25 bu. of beans at 2 qt. for 121¢ will sell for what ? 

19 of a 235-lb. barrel of sugar at 4;4,¢ is worth « dollars. 
zy T. of cream of tartar fills how many 4-oz. boxes ? 

322 yd. lace billed at $87 costs how much a yard ? 


6. When hay is $13? a ton, what fraction of a ton is worth $13? 
How many pounds ? 


ot Ff WW WO 


7. When 115 votes are in favor of a project and 46 are against 
it, what part of the whole are opposed ? 


8. Find the gain in 2250 lb. of wool bought at 161¢ and sold at 
163 ¢. 

9. A man sold 2 of his interest in a mill for $30. If his share 
amounted to 3 of the whole property, what part of the whole did he 
sell? What was the value of the whole property at this rate ? 


10. Broadway Park measures + of a mile wide and 3 of a mile 
long. What will a walk 8 feet wide around the park cost at 621¢ 
per running foot? (Draw a diagram. Do not leave the corners 
without a walk.) 


11. If = of a piece of work can be done in 3 of a day, how long 
will it take to complete the work ? 


12. At an auction one buyer bids + of the cost, another 4. The 
difference was $75. What did each bid ? 


13. If a glass jar contains a hundred thousand fish eggs, how 
many jars will hold 8,000,000? If 13 are hatched, how many on an 
average are lost from each jar ? 


14. The catch of shad for a certain period is valued at $145,000. 
What part of this is $4000, the cost of hatching the eggs and stock- 
ing the waters ? 


15. When oysters yield 11 gal. to the bushel, a 25-gal. barrel can 
be filled from x bushels in the shell. 


wo wn 


4. 


DECIMAL FRACTIONS at 


(Review pp. 5 and 6) 
By a decimal system we mean what ? 
Compare the values of the 2’s in 222. 
Compare the values of the 3’s in 33; in 3.3; in 0.33; in 0.033. 


Which of the preceding numbers are integers? Decimals ? 


Mixed decimals ? 


5. 


6. 
T. 
S: 
2: 
10. 
Li 


The value of a figure depends upon what two things ? 
7654321 .234567. 

What figure stands for tenths ? Hundredths? Thousandths ? 

Compare the position and value of the 3’s. Of the 5’s. 

Of what orders are the 6’s? The 7’s? 

What is the use of the decimal point ? 

How is the denominator of a decimal fraction determined ? 


Write the following with denominators: 0.24, 0.08, 0.175, 


0.036, 0.0025, 0.0001, 0.00017. 


12. 
13. 
14. 


8 8 8 ] j ? 
Are 38, 730) ayy Common or decimal fractions ‘ 
How would you write them decimally ? 


Compare the number of places each takes up with the number 


of zeros in the denominator. 


15. 
16. 
ies 


What part of 140.040 should be read first ? 
Where is “and” used in reading mixed decimals ? 


Which is the easier way of finding the denominator of 0.040, 


(a) by counting from the decimal point, — “tenths,” “ hundredths,” 
“‘thousandths,”’ — or (0) by imagining 1 and three zeros annexed ? 


Read : — 

18. 0.507, 0.0307. 21-5, O-7105'0.0071: 

19. 330.03, 0.303. 22. 64.0019, 6400.019. 
20. 3003.075, 3.00375. 23. 6000.006, 0.6006. 


(4 DECIMALS: READING AND WRITING Oral 


Since 84 per cent, or 84%, means 84 hundredths, or 0.84, in what 
two ways might the following be read ? 


1. 0.06, 334%, 0.163. 3. 0.871, 871%, 0.004. 
2. 0.14, 0.374, 413%. 4. 0.00%, 2%, 0.064. 


5. 34 thousandths is written 0.0034. To what order of units 
does the 4 belong? 


6. 1% is written 0.004. Write 2%, 14%, 24%. A number 
made up of decimal and common fractions is a complex decimal. 


7. Give other complex decimals. 


Writing Decimals 


1. If the denominator contains three zeros, how far from the 
decimal point must the numerator end? 


j ; 1 F 845 12 S17 1264 
2. Write decimally: 345, 24%, 24> ith: 
3. If the numerator contains but one figure and the denominator 


three, where is the numerator written? What is written in the 
other two places ? 


W 1 . 3 1 9 5 19 

4. rite: T0002 T0000? T00? T00009 10002 10000° 
Wri ° 3 20 1 1 a 24 

5. rite: 1 100? 2 Orb Sido Ortiv: 


6. Write as common fractions or mixed numbers: 1.003, 20.020, 
19.03, 0.0013, 125%, 250%. 


Write from dictation or at sight : — 


7. 8 thousandths. 12. 804 hundred thousandths. 

8. 17 tenths. 13. 400 and 4 ten-thousandths. 

9. Threeandafifth %. 14. Forty thousand forty millionths. 
10. 3075 millionths. 15. Seven hundred six thousandths. 


11. 4a hundredth. 16. Two million 71 and 404 millionths. 


Oral DECIMALS: ANNEXING ZEROS 13 


1. Change 12 to larger units. What principle applies? 


2. Annex a zero to 0.8. Write 0.8 and 0.80 as common fractions 
and compare their values. 


3. Compare the numerators, the denominators, and the value of 
0.90 and 0.9. 


4. What effect on the number of units has annexing a zero toa 
decimal ? What effect on their size ? 


5. Omit the zeros at the right of 0.860 and 0.400. How is the 
numerator affected? The denominator? The value? 
Read as printed; then in smallest decimal terms, that is, in largest 
decimal units : — 
6. 0.0400, 6.6450. 8. 8.0500, 0.050. 10. 9.400, 0.100. 
7. 7.0900, 0.0600. 9. 10.010, 8.450. 11. 0.50, 0.050. 


12. What is the effect upon the value of a number when the deci- 
mal point is moved one place to the deft? One place to the right ? 


13. If a zero is annexed to 8 is the decimal point moved? 
Which way ? 


14. To 1.2 annex a zero. Is the decimal moved, that is, have 
ones and tenths been changed ? 


15. Tell how each figure is changed in value when a zero is an- 
nexed to 135. To 13.5. 

16. Explain any change in value made by annexing a zero to 8; 
to 120; to 0.3; 0.03. 

Read the following as printed; then with one or more zeros 
annexed ; — : 

bie Odie 7.9- "0.07? 0.10 0.008; 245.6; 36.008. 

18. Read and announce the change when the decimal point is 
moved one place to the left. 


19. When the decimal point is moved one place to the right. 


74 DECIMALS CHANGED TO COMMON FRACTIONS Oral or Written 


1. 0.75=745,=%. Give directions for the two steps in this 
process. 


Change to common fractions. Give each step. 


2. 0.2, 0.4, 0.5. 5. 0.125, 0.480, 0.375. 
3. 0.80, 0.25, 0.12. 6. 0.000125, 0.0625. 
4. 0.50, 0.75, 9.70. 7. 0.00375, 0.001728. 


2 100 e100 1 e100 meee 


9. Multiplying both terms of 7 by 4 has what effect on the 


00 
value? On the form? Upon what principle does this depend ? 


Aare nT Oe | 


10. Explain the whole process of reducing a complex decimal to 
a common fraction. 


Change to common fractions : — 


11. 331%, 0.162, 662%. 14. 0.031, 41%, 0.061. 
12. 0.834, 0.081, 584%. 15. 62%, 311%. 
13. 121%, 0.37h, 874%. 16. 412%, 0.621, 912%. 


Change the following per cents to common fractions : — 
17-26. 43¢%, 504%, 623%, 682%, 814%; 413%, 
933%, 228%, 291%. 
27-36. Subtract each of the preceding from 100% and change the 
remainder to a common fraction. 
37. Change ¢ to 100ths or %. 
gig LOO P00 = Bote 
* 800 800+8 100 


PRACTICAL CALCULATION 28 


= 0.874 = 871%. 


dare ae a Sits 41, 27, 44, 15, 

ee Boo , p. 145. 

8) 7.000 39s, AQT S.. Cte 
0.875 = 874%. 40. 50: 43. si. 46. 5. 


Written ADDITION AND SUBTRACTION OF DECIMALS Tits) 


1. Without copying, write the sum of each column and of each line. 


whe 2. 3. 4. 5. 
6. 96.475 + 186.52 + 0.4875 + 0.64985 + 396.47. 
7. 83.8 + 62.379 +293 +3.207 + 82.379. 
8. 542 + 48 +8479 + 0.0439 4+ 64. 
9. 16.783 + 9.54 +653 +9.642 + 180.09. 
10. 4.09 + 72.683 + 2.946 + 8.78514 + 34.769. 


Il. Find the difference, first explaining whether the denominators 
must be alike: = 


ie 2. 3. 4. 5. 6. 
7. 3.64 — 1.878. 9. 41. —13.074. 11. 6389 — 0.497. 
8. 19 — 0.5694. 10. 9.87 — 4.3. 12. 2.641 — 0.0994. 


13. Take seventeen hundred eight ten thousandths from twenty- 
four and six thousandths. 


14. From eighty-six tenths take forty-three thousandths. 


III. Rewrite as integers and decimals; then add each column and 
each row : — | 


Ds 2. Os 4, 5. 6. 
7. 16.372 85 79.42 144 863 21.054 
8. 2161 B41 POTS) Wo rm OTe Wah 1 6:25 
Oeeeb te 0.8470 wy 964: 20 omen 621%, 
10. 3 871% 0.758 931% 4 1219, 
Lise OS 2.08 15 695 116% 6.4837 


IV. Find the difference between : — 


1. 17.38 and 200. 4. 94 and 7969. 7. 1 and 0.833. 
2. 2.0875 and 3. 5. $5 and 24. 8. 0.1 and 0.0833. 
3. 44 and 7.011. 6. 2 and 64%. 9. 10 and 8.31. 


76 MULTIPLICATION OF DECIMALS Oral 


1. Compare 3 and 0.3. Moving the decimal point one place to 
the left has what effect ? 


2. Move the point one place to the left in 18.4 and 0.15, and give 
the result and the effect on the number, 


3. Compare 0.1 of 18.4, 4 of 18.4, and 18.4 + 10. 
4. Find 0.1 of the following: 3.4, 0.2, 0.05, 12.5. 


5. Compare 400 and 4.00. Moving the point two places to the 
left has what effect ? 


6. Read the quotients after dividing these by 10. By 100. 
24.5, 8.65, 42.1, 0.04, 0.875, 625, 0.264, 1.82. 
7. Instead of reading the preceding as divided by 10 or 100, we 


may read them as or of the number. 
Give at sight : — 
8. +1, of 2.46. 10. aby Of 37.6. 12. 0.0001 of 3500. 
9. 0.010f 32, 11. 0.001 x 0.9. 13. 0.001 x 25. 


14. Having found 0.1 or 0.01 by moving the point, how would you 
find 0.3 or 0.05, ete. ? 


15. Compare 0.1 and 0.8; 0.01 and 0.15; 0.01 and 0.08. 
16. What is 0.01 of 300? 0.03 of 300? 


17. 0.01 x 32.45 = what? How many decimal places in the 
result ? 


18. 0.09 x 0.03 = what? 19. 0.06 x 300. 
0.01 x 0.03 = 0.0008 (why ?) 20. 0.15 x 0.6. 
0.09 x 0.03 =9 x 0.0003 (why?) 21. 0.05 x 0.005. 


22. Compare the number of decimal places in the product with 
the number in both factors. 


The product contains as many decimal places as there are in both its 
Jactors. 


Oral 


MULTIPLICATION OF DECIMALS 17 


Wee O.0 Of oUies OC Seve 
2. 334% of 60 =4 of 60. Why? 


Give 


ao a - WwW 


lat 
12. 
13. 
14. 


16. 


2.008 
3.46 


results and show what process you use :— 


. 0.06 of 200. 5% of 500. Te) x 0,0: 2.5 X 0.30. 

. $90 x 0.9. 12% of 1000. 8. 80% of $400. 16% of 40. 
GOL O00 Vator st, 9. 334% of 360. 0.2 x 0.2 x 0.2. 
. 0.08 x 0.5. 20% of 60 yr. 10s cewek, 200 x 0.003. 


Had you first to multiply or divide in these examples ? 
A man of 50, spending 30% of his life abroad, is at home w@ yr. 
2% of $5000 being counterfeit, the rest or $a is good money. 
23 X 375 = 8625. 15. 0.23:x 37.5=y. 
Bo Oe =a, 20 KO. D =z. 

w X 3.75 = 0.8625. 230 Xu =8625. 
How would you write the product of 0.02 x 0.004 ? 


Written 
3.46 x 2.008. 


WorK 


2.008 ExpiLanatTion. The first partial product is 0.06 x 
3.46 2.008 or 0.12048, which may be written in either of 


12048 12048 the ways given. The important thing to remember 


8052 
6.024 


8032 is how to determine the number of decimals in the 
6.024 product and to put the decimal point where it belongs. 


6.94768 6.94768 
(a) Why are there 5 decimals in the first partial product, 4 in the 
second, and 3 in the last ? 


2. 
3. 
4. 
Ly 


0.84 x 5.076. 5. 0.0874 x 12.50. 8. 8% x $456. 
8.47 x 9.432. 6. 1.8% x 0.360. 9. 0.24 x $9.60. 
0.84x $9.60. 7. 0.86x36x36. 10. 17% x 34.6. 


A man’s salary is $1200. If reduced 121%, what will it be? 


72 DIVISION OF DECIMALS Oral and Written 


0.48 + 8, or 4 of 0.48 = —— hundredths or 0.—. 

0.48 + 0.06. Have these a common unit? What is it? 
What is 4 of 0.81? £o0f0.072? 1 of 0.063? 
Whatis6.5+7? 81+9? 105+7? 

Compare 0.8+0.4 with 8+4. 20+4 with 10+ 2. 

Does multiplying both dividend and divisor affect the quotient ? 


Compare 0.049 + 0.07 with 4.9+7. How many places to the 
Jai was the point moved in each? By what did this multiply each? 


Pe CFO een Vat es 


8. When any number of units (dollars, feet, tenths, hundredths) 
is divided into any integral number of parts, what is the unit of 
each part ? 

9. Then if the divisor is an integer as in 4.9+7, the quotient . 


will be expressed in the same units as the Hence 4.9 + 7, or 
AY tenths, +7 =0.7. 


To divide 0.144 by 0.09. 

10. In the example at the left how 
is the divisor changed from 0.09 to 9.? 
For what purpose ? 

To divide 63.44 by 25.6. 11. How and why must the dividend 

Process also be changed? State the principle. 
2.47 + 12. After dividing 14 by 9, how 
25.6)63.44 256.) 634.4 many tenths in all remain to be divided? 


PROCESS 


0.09) 0.144 =9.)14.4 
1.6 


512. 13. Explain the process shown in 
122.4 the second example. When there is a 
102.4 remainder, how do you continue the 
20.00 division ? 

Le 


14. How may you always have an 
eu. integral divisor ? 


15. 38.7 + 4.34. 16. 3.485 + 0.95. 17. 24.6 + 0.17. 


Principle. Multiplying or dividing both dividend and divisor by the 
same number does not affect the quotient. 


Written DIVISION OF DECIMALS 79 


Give directions for division of decimals in five steps: — 
I. Setting down. II. Pointing. III. Dividing. IV. Placing 


and pointing the quotient. V. Managing the remainder. 


Divide, noticing whether the quotient will be larger or smaller than 
the dividend : — 


1. 21.6 + 0.006. 6. 102.01 + 1.01 +12.5% of 100. 
2. 0.4913 + 1.7. 7. $8.281 + 23, — 6.25% of $3.00. 
3. 2.1952 + 0.028. 8. 4.096 + 0.0064 + 0.82369 -+ 28.7. 
7 yee) 9. 67.24 x 82% — 67.24% + 82. 

5. 0.6345 + 0.009. 10. 400 + 0.662 + 876.16 + 0.296. 


Common Fractions Changed to Decimals 


Since 3 + 8 or ¢ of 3 = 3, a fraction may be changed to a decimal 
by considering it a problem in division of decimals; thus, — 


& = 8)3.000 


0.375 

Change to complex decimals of three places: — 

es Lees 19k 4e) 23.85. 

12. 5%. 16. 35. 20. 83. 24. 48. 

VS tear. Lyd Dod ae 25. 16. 

14 he 18. 23. a2 0443) PAO Ee 9 
Change to incomplete decimals of four places : — 

yin nae. 2970 ao, Vie ey B3rete 

28. 2. 30. At. 32. gt. 34. +35. 

35. A long ton is 224° of a short ton. Express the relation as a 


mixed decimal 


36. 9 is what part of 144? Express the relation as a complex 
decimal of two places. As a per cent. 


37. What per cent of $6000 is $4680 ? 


80 REVIEW EXERCISES Oral 


1: 88.025 is to be divided into 195 parts. Will each part be 
more or less than 4+? 


2. How many places would there be in the quotient if the division 
were exact ? 


3. A camel goes 3.5 miles per hour. How far will it goin 10 hr. ? 
4. Of what two equal numbers less than 1 is 0.25 the product ? 
5. Find the square root of 0.0081. 

6. 12 is what per cent of 50? Of 25? 


7. Find the balance of this account by inspection. Which party 
is described as Dr. and Cr. ? 


New Yorks, Jan. 30, 1904. 
Mr. J. Q. ADAMRB. . 


In acct. with Joun ReEynoups & Co. 


Dr. Cr. 


Jan. 2 | To Mdse. as by bill || $114 | 81 Jan. 1 | By bill for services || $150 | 00 


9 | Freight prepaid 2 | 13 5 | By goods returned 14; 81 
Storage of barrels 50 By allowance for 
16 | Cash on acct. 50 | 00 damages 2 | 00 


8. Multiply the sum of 11.507 and 4.493 by the difference between 
10.85 and 103. 


Read rapidly and change to or from decimal forms : — 
425%, 0.0006, sf 

. 20.2020, 202.020, 2020.20. 
0.12, $10.012, $412. 


35 1000, 


3 
$) EVO) B00? 15 ee 


i 


900 
100 
. 0.314, 0.0374, 3.74. 


6 
2 7 
3. 68%, £%, AL, LH. 8. 1 
4 9 
5 


19104 40800 _985 
100M MO LOKOrOis 


. 60,004, 0.048, 6.666-+. 10.) gate eee vat On 


Written REVIEW EXERCISES 81 


1. A city contains 40,000 persons, 26% in the first ward, 32% in 
the second, 21% in the third, and the remainder in the fourth. How 
many in each? 


2. 21% of a gang of 200 workmen receive $48.30. The wages 
of the rest are 20% higher. What does a workman of each class 
receive per day ? 


3. The binding of 390 books cost $54.60. What was the entire 
. cost of each copy if the binding was 14% of it? 


4. 164 ft.=1 rd. One girl lives 370 rd. from school; another 
142.35 rd. on the same road. ‘Their houses are how many feet apart ? 


5. When the cost of transporting coal is 2 ¢ per ton for each mile 
the freight on 400 tons is $800. What is the distance ? 


6. At 1.25 cu. ft. to the bushel, compute the value at 571¢ a 
bushel of a bin of corn containing 4000 cu. ft. 


7. Find the profit on 274 bbl. of flour at $4.114, and 128 bbl. at 
$ 3.963, if sold at 3¢ per pound. (196 lb. to the barrel.) 


8. After melting 2 of a sheet of metal, and later 4, there was 44 


of a square foot left. How many square inches in the part first 
melted ? 


9. £1 English money = $4.8665. ind the value of £23,738. 


10. $81,271.08 is to be divided among 7 heirs. 65 of them share 
equally; the others receive each a double portion. What is the 
amount of a 2% tax on 1 of the 5 equal shares ? 


11. A lot of cord Mont is =8, beech, 0.21875 birch, 0.1875 maple, 
35 ash, 10 cords oak, 4 poplar, and 34% pine. How many cords 
in all? 


12. When 5.20 francs = $1, how many dollars will 3302 francs 
equal ? 


82 INTEREST: GENERAL METHOD Oral 


1. I live in a hired house worth $6000. For the use of the 
house for a year I pay ;45, or 10%, of its value. What do I pay per 
year ? 


2. If I had used the money which the house cost, $6000, for a 
year at the same rate, 10%, the annual interest would have been 
what? The interest for 6 mo. would have been what ? 


3. The value of a house used was $3000; rate of rent, 5%. Find 
a year’s rent.- A month’s rent. 


4. Money used, $3000; rate of interest, 5%. Find a year’s 
interest. A month’s interest. 


5. What is the difference between rent and interest ? 
Interest 1s an allowance to the owner for the use of his money. 
The principal is the money used. 
The amount is the sum of the interest and the principal. 
The rate of interest is the number of hundredths of the principal 
paid for a year’s use of it. 


6. The principal is $200. The rate is 6%. Give the interest 
for- 1 yr.; 2 yr.3 3.yr.; 4 yr. 35 yr. 3 the interest for 1omos soe 
3$mo.;4.mo.;°5 mo.; 6° moe.;/7 mo.; S$ mo. 9imo0., 10 m0 eee 


7. What is a year’s interest of $300 at 2%? 3%? 4%? 5%? 


| Find the interest : — What shall I pay for the use: — 
8. Of $300 at 4% for 2 yr. 11. Of $1000 for 2 yr. at 10% ? 

9. Of $500 at 6% for 3 yr. 12. Of $600 for 2 yr. at 10% ? 
10. Of $800 at 7% for 4 yr. 13. Of $800 for # yr. at 4%? 


14. In most business transactions 30 da. make a month. If a 
month’s interest is $60, what is the interest for 1 da.? For 10 da. ? 
For 20 da. ? 


15. At 6% the interest of $300 for 1 yr. is 
——. For 1 da. it is 


For 1 mo. it is 


Written INTEREST: GENERAL METHOD 83 


1. Find the interest of $240 for 2 yr. 5 mo. at 5%. 


B 
A 
$ 240 incipal a 
= principa 29 x+y.» yx $949 = 29 
05° = rate # ‘00 : 
$12.00 = int. for 1 yr. 20 
2,5, = time in years (a) In B what represents a 
$5.00 = int. for 7 yr. year’s interest ? 
24.00 = int. for 2 ree (6) A month’s interest ? 
$ 29.00 = int. for 25% yr. (c) How is the process short- 
ened ? 


What is the interest of : — 

2. $840 forlyr.9mo.at10%? 5. $1000 for 12% yr. at 8% ? 
3. $360 for4 yr.10mo. at5%? 6. $400 for 2 yr.5mo.atT% ? 
4. $960 for 1 yr. 8 mo. at 4% ? 

7. Find the interest of $500 for 1 yr. 5 mo. 6 da. at 5%. 


A B 
$ 500 ae 
05 eon $215, 
$ 25.00 =int. for 1 yr. PIP x a * 700 x ae ~——— = $ 35.83 
10.412 = int. for 5 mo. 12 


Al¢ = int. for'6 da. 
$35.83 =int.forlyr.5mo.6da. 6 


(a) Explain the process in B. (6) What is the advantage of this 
method ? 


Find the interest of : — 


8. $600 for 60 da. at 4%. 12. $336 for 8 mo. 10 da. at 4%. 

9. $250for1mo.1dda.at6%. 13. $1728 for2mo.17 da.at9%. 
10. $120 for 80 da. at 7%. 14. $2800 for 9 mo. at 41%. 
11. $372 for 36 da. at 10%. 15. $1000 for 93 da. at 44%. 


To Teacuer. (If drill in interest is desired at this time, see page 156.) 


84 


ae 


MEASUREMENTS: LINES Oral 


Beginning with the shortest, name five units used in measur- 


ing lengths or distances. Give the table of length measures. 


2. 


oO UWO oT PR w 


9. 


Compare an inch with a foot. An inch with a yard. 
Compare a foot with a yard. Witharod. With a mile. 
What part of a mile is a rod ? 


A yard is what part of arod? Ofa mile? 


72; miles = rods. 
Q1 tn, sees in. 
320 x 54 x 3 ft. =1 mi. = —— ft. 


Learn in some way, as measuring and counting your steps, the 


distance from your home to school in feet; in yards; in rods. 


10. 


Estimate in feet the dimensions of your schoolroom. ‘Test 


your estimates by measuring. 


ak 


Estimate and test longer distances as the dimensions of your 


playground in rods; estimate in yards. 


12. 
13. 


At 1¢ per foot, what is the cost of 4 yards of picture wire ? 
At 12¢ a yard, picture molding for a room 25 feet long and 


20 feet wide will cost what ? 


14. 
15. 
aS: 
19. 
20. 
Zl. 


wee 
long ? 


23. 


4rd. = —— ft. 16.1000 .0d. <r ms 

100 in. =a yd. + y ft. +2 in. 17. 4 mi. less 50 rd.=2 rd. 
It is 884 feet around a square. How long is one side of it ? 
32 rods is what part of a mile ? 

A 10-rod tape line is how many yards long ? 

2 of a foot is what part of a yard ? 


How many 4-inch bolts can be cut from a rod of iron 104 feet 


A bicyclist travels 2 rods in a second. How long will he be 


in going a mile? 


Oral - SURFACE MEASURES 85 


A plane surface or a plane, is a flat, level surface. 

The boundaries of surfaces are lines. The sum of the lines bound- 
ing a surface is called its perimeter. 

Surfaces bounded by straight lines are called rectilinear surfaces 
(rect- meaning right or straight). 


1. What is the shape of the common units of surface measure ? 
2. Describe a square. Draw a square inch or a 1-in. square. 


3. Name the five square measures of surface, beginning with the 
smallest and giving the length of each. 


4. An acre is not a square unit of measure; it contains 
square rods. 


5. What is the length ates a square yard in yards? Infeet? In 
inches ? 


6. Give the length of a square rod in yards; in feet. 
7. Give the length of a square mile in rods; in yards; in feet. 


8.. Draw a diagram of a square foot. If your paper is too small, 


draw to some scale as 4, 4, etc.; that is, represent 1 in. by 4 in. or tin. 


9. Divide your diagram so as to show the number of square 
inches in a square foot. How many are there ? 


10. 3sq. ft. = sq.in.; 4sq. ft. = sq. in.; 4 sq. ft. =—— 
Sq. in. | 
11. 1 sq. ft.=——; 4 sq. ft. =——-; +, sq. ft. =_——_. 


12. Represent a square yard onascale of 1. Separate into square 
feet. How many are there ? 

13. Draw a diagram to represent a square rod. Let 1 in. represent 
a yard. What scale is this? 

14. You will find squares, half squares, and —— quarter 
squares. How many square yards in all ? 


15. Outline a square rod on the schoolroom floor or in the 
school yard. How many feet OS it? How many square feet 
does it contain ? 


86 SURFACE MEASURES Oral and Written 


16. Draw a figure to represent an acre, 10 rd. wide and 16 rd. long. 
Let 4 in. represent a rod. Divide your diagram to represent square 
rods. How many in an acre? 


17. Lay off an acre in your school yard or in some field near by if 
convenient. Make it 10 rd. wide and 16 rd. long. 


18. Lay off an acre 8 rd. wide and 20 rd. long. 


19. How many acres, or what part of an acre, does your school lot 
equal ? 


20. £ A. = —— sq. rd. 


21. A square mile is called a section. How many rods long is a 
section ? 


22. How many acres in a strip a rod.wide and a mile long ? 


23. How many such strips ina square mile? Then “how many 
acres in a square mile or section ? 


24. A western township is 6 mi. square. How many square miles 
does it contain? How many acres ? 


TABLE FOR SURFACE MEASURES 


12? or 144 square inches (sq. in.) = 1 square foot (sq. ft.) 


32 or 9 square feet = 1 square yard (sq. yd.) 
(53)? or 304 square yards = 1 square rod (sq. rd.) 
160 square rods = lyacre (A;) 

640 acres = 1 square mile (sq. mi.) 


25. Change 20,000 sq. in. tosquare feet. 29. 1 sq. rd.=~-2 sq. ft. 
26. Change 12,371 sq. ft. tosquarerods. 30. 5 A.=~2 sq. ft. 

27. Change 287 sq. rd. to square feet. 31. 200s8q. yd. = a sq.rd. 
28. Change an acre to square feet. 32. 1900ISq. T= eras 


33. Bought 7 A. for $400 and sold it at 10¢ per square foot. 
How much did I gain or lose ? 


34. In 20,000 sq. ft., how many square rods ? 


Oral LINES AND ANGLES 87 


1. Straight lines that lie in the same plane, and that cannot 
meet however far extended, are parallel, 4 B 
as AB and CD. 6; D 


2. When two lines meet, they are said to form an angle. 


3. The lines are called the sides of the angle, and the point 
where they meet is the vertex. U 


4. In reading an angle, we read a point on one 
side, then the vertex and a point on the other side, 
reading around contrary to the motion of the hands ?* “A 
of a clock. ‘Thus the angle in the margin is read angle ABC. Or 
since there is but one angle at B, it may be spoken of as angle B. 


5. To measure an angle is to measure the difference of direction 
of its sides. If BC were to start from the position BC and revolve 
about B as a pivot until it again came to the position BC, it has 
revolved through 560 degrees (360°), or made a complete revolution. 


6. If two straight lines intersect, they form 4 angles. 
If these angles are all equal, they are right angles. 
How many degrees in a right angle? 


7. Lines forming right angles with each other are 
perpendicular. 


8. If you prolong the sides of an angle, do you increase the size 
of the angle ? 


9. Angles not right angles are oblique. 
10. An oblique angle less than a right angle is acute. 
11. An oblique angle greater than a right angle is obtuse. 


Two angles having a side in common are adjacent angles. 


TEVA 


right angle acute obtuse adjacent angles 


88 ANGLES | Oral 


1. Angles are measured by a protractor. The center O is placed 
at the vertex, 
and the magni- 
tude is read on 
the scale —be- 
tween the two 
sides. Thus, in 
the figure, angle 
ABC is 50°. 

2. Every de- 
gree contains 60 minutes (60’), and every minute contains 60 seconds 
(60"). 


preys ee! 


TABLE 
60 seconds ('') = 1 minute (’). 
60 minutes =1 degree (°). 
360 degrees = 1 revolution. 
90 degrees = 1 right angle. 


3. Draw angles of 90°; of 45°; of 60°; of 120°; of 105°. 
4. Which of these are acute? Which obtuse? Measure them. 


The Six Quadrilaterals 


1. A figure bounded by four straight lines is a quadrilateral 
(quattuor four, latus a side). 

2. There are three classes of quadrilaterals, namely, (a) those 
with opposite sides parallel; (b) with one pair of sides parallel ; 
(c) with no two sides parallel. 


aa Se 


3. A figure in which the opposite sides are parallel is a parallelo- 
gram. Are A, B, C, and D parallelograms ? 


Oral QUADRILATERALS , 89 


4. Describe A as to sides and as to angles. 


5. A figure whose sides are equal and whose angles are right 
angles 18 a square. 


6. Describe B as to sides and angles. 
7. A parallelogram whose angles are right is a rectangle. 
8. Is darectangle? Is B? Is Ba square? 
A square may be said to be an equilateral rectangle. 
9. Describe C as to sides; as to angles. 


10. A parallelogram whose sides are equal, but whose angles are 
not right angles, is a rhombus. 


11. Describe D as to sides; as to angles. 


12. A parallelogram whose angles are not right angles is a 
rhomboid. Is C’ a rhomboid? 


A rhombus might be called an equilateral rhomboid. 


Notre. One generally speaks of a figure like D as a parallelogram, and gives 
to any of the other three special parallelograms its proper name, as square, 
rectangle, or rhombus. 


18. Which of the parallelograms are equilateral ? Equiangular ? 


14. Any side upon which the parallelo- A D 
gram is supposed to stand is its base. That 
which shows the height of a parallelogram 
is its altitude. 
In the figure BC is the base and AH the 
altitude. ja Ait C 


15. The altitude and base are always perpendicular to each other. 


16. The straight line AC joining the vertices of opposite angles 
is a diagonal. What other diagonal has the parallelogram ABCD? 


17. By cutting, compare the two figures into which a diagonal 
divides a parallelogram. 


90 QUADRILATERALS Oral 


18. Prove by cutting accurately from cardboard that — 
(1) A diagonal bisects a parallelogram. 
(2) The opposite angles of a parallelogram are equal. 
- 19. Prove by measuring with a protractor that — 


The sum of the angles of any quadrilateral is equal to 360 degrees, 
or four right angles. 


E . F 
20. A quadrilateral having but one pair of sides parallel, as in 
Fig. 1, 1s a trapezoid. 
21. If no two of the sides of a quadrilateral are parallel, the 
figure is a trapezium. 
The Measurement of Rectangles 
1. A rectangle 1 in. wide and 5 in. long contains how many 
square inches? (See figure.) 
2. A rectangle 4 in. wide and 5 in. long will contain how many 
rectangles 1 in. by 5 in. ? 
3. How many square inches in a 
rectangle 4 in. wide and 5 in. long? 


4 in. 


4. What is the area of a rectangle 8 in. 
wide and 15 in. long ? 

5. A rectangle a foot wide and 20 ft. 
long contains how many square feet? <A Sim, 
rectangle 12 times as wide and the same length will contain 
Lo sq. ft. 

6. Find the area of a rectangle 15 ft. long and 7 ft. wide. 

7. Find the area of a rectangle 8 ft. by 15 ft. 


Oral, Written . THE MEASUREMENT OF RECTANGLES 91 


8. Hind the area of a square rod in square feet; in square yards. 


9. A piece of land measures 20 rods one way and 25 rods the 
other. Find its area in square rods; in acres. 


10. A kindergarten table 4 ft. 3 in. long and 20 in. wide is marked 
off in square inches. How many are there? 


11. Ina flag 10} feet long and 3 as wide how many square yards 
of bunting, not allowing for seams? 


12. A patchwork quilt 3 yards square is made of 4-inch silk 


squares. How many are there ? 


SuGcEstTion. How many squares in a strip 1 square wide and 3 yards long ? 
How many such strips in the quilt ? 


13. What is the area of + mile of street 4 rods wide ? 


14. A lot of land 56 ft. by 125 ft. is sold at 493 ¢ a square foot. 
Required the proceeds of the sale. 


15. A swimming tank is 40 ft. long and 18 ft. wide. What will 
it cost to cement the bottom at $2.25 per square yard ? 


16. A city block is 600 ft. long and 2? as wide. How many acres 
does it cover ? 


17. A half a mile of 60-ft. street is paved with granite blocks. 
How many will be required at the rate of 36 to a square yard ? 


18. What will a sheet of zinc 8 feet long and 32 inches wide cost 
at 71¢ a pound if every square foot weighs 8 ounces ? 


19. Estimate the cost of the blackboards in your schoolroom at 
75¢ a square yard. 


20. What shall I pay Mr. Bates for concreting a wall 60 ft. long, 
4 ft. wide half the length, and 3 ft. wide the rest of the way? The 
price is 75¢ a square yard. 

21. Ifa city lot containing 3750 square feet has a frontage of 50 
feet, how deep is it? 


92 CARPETING, TILING, ETC. Oral and Written 


1. Ingrain carpets are generally woven in strips 1 yd. wide; 
other carpets 3 yd. What two advantages come from running the 
strips lengthwise of the floor rather than across it ? 


2. On floors of the following widths, which of the two widths 
(1 yd. and # yd.) could be used without cutting or turning under any 
strip ? 
12 ft. 15 ft. - 22% ft. 27 ft. 134 ft. 20, ft. 18 ft. 


3. How many strips of ingrain carpet are néeded to carpet a 
room 18 ft. square? How many yards in each strip? In all, if 
there 1s no waste in matching? 


4. How many strips of brussels or tapestry are needed for a 
room 15 ft. by 21 ft.? How many running yards in each strip? 
How many in all, if there is no waste in matching? Find the 
cost at $1.25 per yard. 


5. How many strips of ingrain will be needed to carpet a room 
14 ft. by 20 ft., the strips to run lengthwise, no strip to be cut? 
How many yards in all, if there is no waste in matching ? 


6. On the same conditions, what will brussels 3? yd. wide cost at 
$1.50 per yard ? 


7. What will 4 ft. of oilcloth cost for the same room at $1? In 
this case, would it be cheaper to put the strips crosswise? Why? . 


Find the cost of carpeting floors under the following conditions 
(strips that are cut cost as if whole) :— 


Length of Width of Width of Allowance for Cost per 
Room Room Carpet Matching Yard 
8. 18 ft. 14 ft. 1 yd. 11 yd. $ 0.90. 
9, 22 ft, 18 ft. & yd. 21 yd. 4.25, 
10. 163 ft. 134 ft. 1 yd. q yd. 0.872. 


iti yea ee 20 ft. 8 yd. 28 yd. 1.372. 


Written RECTANGLES: TILING, ROOFING, ETC. 93 


1. Find the area of two surfaces repre- 
sented at the right. (6'4" = 5 ft. 4 in.) 


2. How many tiles 2 in. square will 
be required to cover them ? 


3. How many rolls of paper 8 yd. 
long and 18 in: wide will be required for 
a room 134 by 18, and 8 ft. high, if no 
allowance is made for doors, windows, 
and baseboards ? 


4. 91 squares of slating are required to cover a certain roof. 
This is equal to how many square yards? If the slates are 8 x 16, 
and each course overlaps 10 in. of the one below it, find the 
number of slates used. (A square of roofing or flooring measures 
10 ft. x 10 ft.) . 

5. How many blocks 6 in. x 4 in. will be used in paving a 4-rd. 
Square ? 

6. How many tin plates 13 in. x 19 in. must be used for 1 square 
of roofing, if they are lapped or folded 4 
in. on each side ? 

7. Three piazza roofs about a house 
measure in feét 30 x 8, 24x 7, 74 x 123. 
How much more than 5 squares do they 
contain ? 


8. A house lot contains 1 A. How 
many square feet? The house is 274 x 40. 
What would it cost to sod the remainder 
at $1.50 a square? 

9. Let this figure represent the outline 
of a cellar. Copy, and divide it into 5 
réctangles. From the given dimensions 
find those of each rectangle. 


10. How many square yards of cement would be required to 
cover the bottom of the cellar? 


94 RECTANGLES Oral 


1. A chessboard contains 64 squares 11 in. long. What is 
its perimeter? If it has an inch-wide border, what is the entire 
perimeter ? 

2. Ina 2-in. square how many }-in. squares? How many 4-in.? 


3. Compare the perimeter of a 4-ft. square and an equal surface 
8 ft. long. (How wide is the latter surface?) 


4. My sidewalk is 10 ft. wide besides the curb, and 100 ft. long. 
How many 4 x 8 bricks in it? | 

5. Compare a 4-in. square and a 12-in. square as to length 
and area. 


6. A marble slab 4 ft. by 21 ft. was sold for $4.50. Find the 
price per square foot. 


7. What is the area of a square that can be set off with 200 ft. 
of rope ? 


8. How many boards 9 in. wide will-make a close fence 8 ft. high 
around three sides of a square lot 180 ft. long ? 


9. A hall measures 12 ft. by 36 ft. How many breadths of 
yard-wide carpet would be needed? How many yards, allowing 
3 yd. waste in matching the pattern ? | 


10. A room 14 ft. by 18 ft. 1s to be covered with yard-wide carpet 
at $1 ayard. Which is the cheaper way to run the strips? Why? 


11. A rectangle twice as long as wide contains 512 square feet. 
What is the least number of squares into which it can be cut ? What 
will be the area of each square? The length of each? What, then, 
are the dimensions of the given rectangle ? 


12. A rectangle 3 times as long as wide contains 108 sq. ft. 
Find its dimensions. 


13. A rectangular room contains 192 sq. ft. The ratio of the 
length to the width is the same as 4to3. What are the dimensions ? 
Hint. What are the least number of squares into which the floor 
can be divided ? 


Written p MEASURING CITY LAND 95 


SPRING 


POPLAR 
MAPLE 


=i LELAND 
1. Mr. Sharp bought land bordering on Spring Street, between 
Poplar and Maple, at 3¢ per square foot, which he cut up into 


building lots. He first laid out a 40-ft. street in the rear, which he 
called Leland Street. - What did he pay for the land ? 


2. He sold lot C to a civil engineer for his services in surveying 
and making plans, at a profit of only 2¢ per square foot. What did 
the lot sell for ? 


3. The grading of Leland Street cost him $3.75 per square rod. 
What did the street cost him, including land and labor ? 


96 MEASURING CITY LAND ; Written 


After reserving lot A for his own buildings, he sold the rest at 
the following prices per square foot : — 


Find the proceeds of the sale of each lot. 
4. Lot Bfor12i¢. 7. Lot & for 182 ¢. 10. Lot J for 193 ¢, 
5. Lot Dfori5¢. 8. Lot G@for 21”. 11. Lot K for 178¥. 


6. Lot E for 223¢. 9. Lot Hfor 20i¢. 12. Lot LZ for 251¢. 

13. Before the sale, he opened and laid out a 16-ft. alley from 

Maple Street to Leland. What did the alley cost him, $85 being 
paid for labor ? 


14, Mr. Sharp laid a sidewalk 8 ft. 8 in. wide on two sides of his 
own lot A. The 8-in. edgestones cost him 60¢ per running foot. 
The brick cost $12 per thousand, and the labor $58.25. The bricks 
were 8 x 4 x 2, and laid flat. What did the walk cost him ? 


15. The owner of lot J paid $3.30 per rod for fencing hts lot. 
What did it cost if he paid fer only half of the division fence ? 


16. The abutters combined and concreted the alley at 561¢ per 
square yard. What was the total cost ? 


17. What part of the whole cost should the owner of lot J pay ? 
How much did it cost him ? 


18. What does it cost the owner of lot 7? 


19. Leland Street is accepted by the city and paved at a cost of 
$3 per square yard, the abutters agreeing to pay 25% of the cost of 
the part adjoining their property. What is the assessment on lot 1? 


20. What will a walk 8 ft. wide around the whole block cost 
at $1.25 per square yard? Do not leave the corners without a 
walk. 


21. What will it cost to fence lot Jat $1.25 a vod ? 


Oral and Written TRIANGLES 97 


A B C D E 
1. Surfaces bounded by three straight lines as those at the top 
of the page are triangles (¢77 = three). 


2. Triangles are named from their largest angles. They are 
atute, right, and obtuse angled triangles. Name one of each shown 
above. 


3. Triangles are also named from their sides as follows :— 
Equilateral, with sides all equal; 
Isosceles, with two sides equal ; 
Scalene, with no two sides equal. 


4. Find a triangle of each kind at the top of the page. Draw 
others of each kind. 


5. A triangle has three corners or vertices. A line drawn from 
any vertéx of a triangle perpendicular to the opposite side, or opposite 
side produced as in C, is called an altitude, and the side is called the 
base. How many altitudes may a triangle have? 


@. Show by measuring with a protractor or by cutting off and 
laying the angles together that — 


The swm of all the angles of any triangle is equal to two right angles, 
or 180 degrees. 


7. How many right angles may a triangle contain? How many 
obtuse? How many measuring 60° ? 

Find thé size of the third angle of a triangle when two angles measure 
as follows : — 

8. 90° and 30°. 10. 65° and 35°. 12. 75° and 374°. 

9. 120° and 40°. 11. 624° and 87}°. 13. 84° and 76°40’. 


98 THE MEASUREMENT OF TRIANGLES Oral 


C Dati G I 
ra 


E M F 
I ih 


We have seen that any kind of an area having straight lines as 
sides, and right angles as angles, can be divided into rectangles, and 
thus the whole area found. We are now to deal with triangles and 
other areas bounded by straight lines, but whose angles are not all 
right angles. 

1. By cutting, compare the two triangles into which a diagonal 
divides a rectangle. 


2. What is the relation of a to 6 in the rectangle above? Then 
what part of the rectangle is the triangle ? 


3. If the dimensions of rectangle ABDC are 10 in. by 6 in., what 
is the area of triangle ABC ? 


4. In II compare ¢ with d; e with f Compare triangle HFG 
with rectangle HFIH. 


5. Compare the base and altitude of triangle HFG with the dimen- 
sions of the rectangle. 


6. If the dimensions of the rectangle are 12 ft. and 8 ft., what are 
the base and altitude of the triangle? What is its area ? 


7. By cutting, show that in an obtuse-angled triangle, as in ILI, 
the triangle is also equal to half a rectangle having the same dimen- 
sions as the base and altitude of the triangle. It is now seen that— 


Any triangle is equal to half a rectangle having the same dimensions 
as the base and altitude of the triangle. 


8. What is the area of a triangle with base 20 ft. and altitude 
isi ri 


MEASUREMENT OF TRIANGLES, TRAPEZIUMS, ETC. og 


Oral and Written 


1. What is the area of a triangle whose base is 12 rods and alti- 
tude 14 rods ? 


2. State your method of finding the area of a triangle. 


Find areas of triangles of the following dimensions : — 


o>) base=40 ity, alt==18 ft; 7. 194 ft. and 24 yd. 
4. Base==60 ft., alt.=25 ft. 8. 38rd. and 221 ft. 
Simbase—~o tt, alt.==9 in. 9. 64 yd. and 13 ft. 
6. Base—41d., alt, =7 it. 10. 34rd. and 6 yd. 


11. Draw or cut out a trapezium, or a quadrilateral no two of 
whose sides are parallel. 


12. Separate it into two triangles 
along one of its diagonals, as AB. 

13. Find the dimensions of each 
triangle and its area. 


14. What will the area of the trape- 
zium be ? 


15. The diagonal of a trapezium is 24 inches; the altitudes per- 
pendicular to it are 18 inches and 15 inches respectively. What is 
the area ? 

16. The diagonals of a given trapezium cross at right angles. 
The point of intersection is 50 feet from the upper end of each 
diagonal. One diagonal is 100 feet long, the other 150 feet. Find 
the area. (Draw a diagram.) 


17. In right triangles the two sides including the right angle, 
are called the legs. If one leg is the base, the other is the altitude. 
Why ? 

18. The legs of a right triangle are 10 and 15 ft. Find the area. 

19. The diagonal of a trapezium is 14 in. The altitudes perpen- 
dicular to it measure 6 in. and 8in. What is its area? 


100 MEASUREMENT OF PARALLELOGRAMS AND TRAPEZOIDS 


Oral and Written 


1. By cutting, find the relation between the two triangles into 
which any parallelogram is divided by a diagonal. 


2. OM, the altitude of the triangle, P C 
is also the altitude of the parallelo- 
gram, and AB is the base of each. 


3. Compare a parallelogram with 
a triangle having the same altitude 
and base. A M B 
4. What kind of parallelogram is shown in the figure ? 
5. Compare a rhomboid with a rectangle whose dimensions are 
the same as the base and altitude of the rhomboid. 
6. How is the area of a rectangle found ? 
7. How, then, may the area of a rhomboid be found when its 
base and altitude are given? 


Find areas of rhomboids with : — | 
8. Base 121 ft., altitude 74 ft. 10. Bes 2hiyd, A418 im 
9. Base 16 rd., altitude 40 ft. 11. A= 84 ft. B= opm 


12. To find the area of a trapezoid whose two parallel sides are 
24 in. and 16 in. and whose altitude is 12 in. If the trapezoid is 
divided as in the figure, what are es iC 
the dimensions of triangle ABO? 
Its area? If DC is taken as the 
base of triangle ACD, what is the 
altitude? The area? What, then, 
is the area of the trapezoid ? 


N 
me 


A 24 B 
Sraremennr, 4 of 24 x 12 + 4 of 16 x 12, or $ of 40 x 12 = 20 x 12, or 240 
13. Notice that since the altitude is the same in each triangle, 

time may be saved by adding the two bases before multiplying by 

half the altitude. State the rule, then, for finding the area of a 

trapezoid. 


Written MENSURATION: REVIEW 101 


1. Name 2 quadrilaterals that are not parallelograms. 

2. The base and the altitude of arhombus are each 16in. Area? 

3. The altitude of a rhomboid is 2 of its 2-ft. base. Area is 2. 

4. One angle of a parallelogram measures 90°. What do the 
other angles measure ? 

5. The parallel sides of a trapezoid are 25 and 37 ft., respectively, 
and the distance between them is 15 ft. Required the area. 

6. The base of a triangle is 174 in., its altitude 8} in. What is 
its area ? 

7. A lot of land has a frontage of 50 ft. The parallel sides are 


perpendicular to this frontage. One of its parallel sides measures 
10 rd. and the other 80 ft. What is its value at 45¢ a square foot ? 

8. A triangular park measures 600 ft. on one side, 300 ft. on the 
other which is perpendicular to it; how many square rods in the 
park ? 

9. Compare the area of a rhombus having a base of 16 ft., and 
an altitude of 12 ft., with that of a 16-ft. square. 

10. The diagonal of a trapezium is 42 in., and the perpendiculars 

dropped to it from the angles are 16 in. and 18 in. respectively. 
Required the area. 


Find the areas of rhomboids : — 


11. Base 138 ft., altitude $ ft. 13. Base 3i yd., altitude 20 in. 

12. Base 20 rd., altitude 50 ft. 14. Base 2640 ft., altitude 4 imi. 

15. The diagonal of a trapezium is 7 yd. The altitudes perpen- 
dicular to it are 24 ft. and 124 ft. What is its area? 

16. What is the area of one of the triangles into which a diagonal 
of a field 10 rd. square divides it ? , 

17. What will it cost to fence a yard in a shape of an equilateral 
triangle 36 ft. long with 4 lines of wire weighing one pound to every 
20 ft. and costing 3i¢ a pound? ‘There are 12 posts, costing 15¢ 
each. 


102 CIRCLES, DIAMETERS, RADII, ARCS, ETC. Oral 


1. An area bounded by a curved line, all points of which are 
equally distant from a point within called the center, is a circle. 


2. The distance from the center to the curve D 
is the radius, and the curve 1s called the circum- E 
ference. In the figure how many radii are 
drawn? Name them. Ve 
3. Any straight line through the center ter- i - 
minating in the circumference is a diameter. 
Is a diameter shown in the figure? Which 
lines are diameters ? C 


4. Into how many equal parts does a diameter divide a circle? 
One half of a cirele is called a semicircle. 

5. Into how many equal parts do two perpendicular diameters 
divide a circle? Such parts are called quadrants. 

6. Any part of a circumference is called an arc. Any part of a 
circle bounded by two radii and an arc is a sector. Name some sectors 
in the figure. Is a quadrant a sector ? 

7. For convenience in measuring arcs, every circumference, whether 
large or small, is divided into 360 equal parts called degrees (360°). 
How many degrees in a semicircumference? In a quadrant ? 


8. Each degree is divided into 60 minutes (60'), and each minute 
into 60 seconds (60"). 


15° =a’. 300! = 2°. An are of 30° contains 2’. 


10° =a", 600" =a’. of a circumference = 2°. 


{oo 


9. Cut circles of different sizes from stiff cardboard or bring to the 
class several circular objects: plates, rings, covers, wheels, or coins. 
Measure very accurately the diameter and circumference of each. 


Nore. To get an accurate measurement of a circumference two pupils can 
work together to an advantage. Take two rulers, one standing edgewise on the 
other as a guide for the circle. Mark a point on the circumference and roll 
through one complete revolution, noticing the distance passed over on the bottom 
ruler, and holding against the second ruler to get a straight path. 


Oral, Written | 103 


RATIO OF CIRCUMFERENCE TO DIAMETER 


10. In each case divide the circumference by the diameter, carry- 
ing the result to several decimal places. 

11. Compare your results. Take all the results that are about 
alike and find the average. 

12. If you have measured and divided accurately, the quotient 
will be 3.1416 nearly. What does this show ? 

13. If the diameter of a circle is 10 ft., what is the circumference? 

14. 3.1416 is the ratio of the circumference to the diameter. It is 
represented by the Greek letter z (pi). 

15. If D=diameter, A =radius, C= circumference, read the 
following : — 


Cee ODD = CO-+ 7, or ean C= 2 Rr, or 27fR. 


T 


Find the diameter or circumference or radius. Forecast the result. 


Goes 20185 Glam. Pome = Auf el) oer 
tT ee UD tb se) sag, 20eE) = LOAN Ca. 
LS ere edie Ca, Ql pts =a 2) Vasa tet ye = we. 


To Finp THE AREA OF A CIRCLE 


(_) AAAnn nnn 


1. Draw a circle on stiff cardboard. Draw two perpendicular 
diameters. Divide each quadrant into two or more equal parts. 

2. Arrange the parts as in B. What figures that you have 
studied do they most resemble? If these sectors were triangles, how 
would you find the area of each? Of all? Compare the sum of 
the bases of all the sectors with the circumference of the circle. 


104 CIRCLES: AREA Witien 


3. Ifthese sectors were triangles, the area of all would equal the atea 
of one triangle with a base equal to and an altitude equal to 
the OR 


, or Area = 


4. While the sectors are not triangles, yet the smaller they are 
made, the more like triangles they seem, and it 1s proven in geometry 
that the area of a circle is actually the same as you have found by 
supposing the sectors to be triangles, that is, 


The area of a circle is the same as that of a triangle having a 
base equal to the circumference and an altitude equal to the radius ; 


Cece 
or 


times the unit of measure. 


5. Find the area of a circle whose diameter is 10 ft. 


SoLturion. C=10 x 3.1416;= 31.416. 
&=43 of 10 = 5 
2 ) 157.080 

78.54 = number of square feet. 


Notre. We must use Cand R as abstract numbers representing the number 
of units. The product will then be an abstract number showing the number of 
units in the area. 


Find the area of circles : — 


6. R= 6 ft., C= —. 8. C=100 ft., D= ——. 
7. D=12 ft. C=——_. O54 C =o¥ DOT, tT aes 
Sj —- CG x R i) [ ° 
Inge =4'== Sane and C=2x Kx, we may multiply by 


2xXxmxX RYE 
») 


fed 


generally used when the radius or diameter is known. 


2X 7X # instead of C, then A= = 7h’, the formula. 

Find the area of circles : — | 
10. dt =" 15 ft. 13. R22) 1d.) 16. C108 Tt) 1S Seer 
1 aaa 1A, Vig— 164 Cle ek 7 (ee 20. = 96 41 
12. C400 mm. 915. Doe 80 Gd) (18s) aeshird, aL. Da cee 


Drawing and Measuring THE CIRCLE 105 


1. Draw a 2-in. circle. Draw two perpendicular diameters. 


2. Compare the four arcs. Connect the points where the diame- 
ters cut the circumference as in the figure. G 
How do these lines compare ? 


3. Lines joining the extremities of arcs 
as AB are called chords. Chords whose arcs p B 
are equal are also equal. 


4. Measure the angles of the quadrilateral 
ABCD. r 


5. What are the two parts into which AC divides the circle 
called ? 


6. The angle ABC is made, or inscribed, in a semicircle, when 
the vertex B is in the circumference and the sides pass through the 
ends A and C of the diameter. Measure the angle B with a pro- 
tractor. How large is it ? 


Any angle inscribed in a semicircle is a right angle. 
7. What kind of figure is ABCD? Why? .- 


8. If you consider these figures made up of two triangles ABC 
and CDA, what is the length of the base of each? What is the alti- 
tude of each? Then what is the area of each? Of the whole 
square ? 

9. What is the area of the circle ? 

10. How much larger is the circle than the square ? 

11. Find the ratio of the square to the circle (4 decimal places). 

12. Observe Problem 8, and give the area of the largest square 
that can be drawn in a 3-in. circle. In a 4-in. circle. 

13. What will be the diameter of the largest circle you can draw 
in a 6-in. square ? 


14. The top of a 4-ft. round table is what part of a 4-ft. square 
table ? 


106 DRAWING AND MEASURING FIGURES 


1. Draw a 3-in. square. On the same base draw a 3-in. 


rhombus. Which has the greater altitude? The greater area? 


G 
2. Draw a rhombus. Draw the diagonals. 


Measure the angles made by the diagonals. 
Compare the lengths into which each diagonal 


divides the other. 
A B 


The diagonals of a rhombus bisect each other at right angles. 


3. If the diagonal AO—12 in. and DB=8 in., find the area by 
considering the figure two triangles. 


4. The diagonals of arhombus are 10 in.and 16in. What is its 
area ? 


5. Using 1-in. lines, make a rhombus with an altitude of 4 in. 
What is the area? 


6. Using 1-in. lines, make a rhombus with an altitude of 1 in. 
What is its area ? 


7. Using 1-in. lines, make as small a figure as you can. What 
is its shape ? : 


8. The area of a rhombus, when the length of the sides is fixed, 
depends upon what ? 


9. Draw a trapezoid, the parallel sides being 14 in. and 2 in. 
One of the other sides 1 in. long is perpendicular to these. Find the 
area by dividing into a rectangle and a triangle; then find the area 
in the usual way. 


10. Draw a rectangle. With the same sides draw a figure whose 
angles are not right angles. What is this figure called? How does 
it compare in size with the rectangle ? 


11. What dimensions would you need to know to find the area of 
the rhomboid you drew in Exercise 10 ? 


12. Draw atrapezium. What dimensions must you know to find 
the area ? 


Oral Review MEASUREMENTS 107 


1. What objects before you are nearest in length to a yard? To 
afoot? Toarod? 


2. How many degrees measure a|_ (right angle)? Can you find 
as you look about you any but [’s ? 


3. After going 4 round a circle, how many degrees complete the 
circle ? 


4. Since the sum of all the angles of a triangle is equal to 2 |’s, 
each of the three equal angles of an equilateral triangle measures 
how many degrees ? 


5. How may the area of a triangular park be found ? 


6. How can you find the area of any surface bounded by 
straight lines ? 


7. How much of an 8-in. square is not covered by a 7-in square ? 
How much not covered by a 6-in. square ? 


8. An area containing 3 sq. yd. contains how many square feet ? 


9. Which is larger, a square or a rhombus with the same 
perimeter ? 


10. What part of a square yard is a mat 4 yd. square? 


11. A room is 2 as wide as it is long. If it is 30 ft. long, how 
many square fee in the floor ? 


12. The area of a trapezoid is 350 sq. ft. The parallel sides are 
30 ft. and 40 ft. What is the distance between them ? 


13. The area of a triangle is 25 sq.ft. The altitude is 5 ft. What 
is the base ? 


14. 7, or 3.1416, is nearly 31 or 22. Using this value, what is the 
diameter of a tree if it takes a string 44 in. long to reach around it? 


15. The diameter of a circle is 103 in. What is the circum- 
ference ? 


108 MEASURING CIRCLES: PROBLEMS Written 


1. A button is 4.7124 in. round. How long a buttonhole is 
required ? 


2. Find the circumference of the base of a lamp chimney that is 
23 in. across. 


3. A circus ring is 414,% ft. round. Find the distance to the 
center in rods. 


4. A hogshead is a little over 121 ft. round the middle. Will it 
go through a doorway that is 3 ft. 10 in. wide ? 


5. If a mountain is 10 mi. round, what distance might be saved 
by tunnelling ? | 


6. A pie is cut accurately into 6 pieces. What is the ratio of 
the curved edge to the straight one ? 


7. The hubs of two wheels are alike, but the spokes of one are 
3 in. longer. How much greater is its circumference ? 


8. Ifa barrel is 8 in. over the chine, how much strap iron will be 
required to make 100 end hoops with 3-in. laps? Make a statement. 


9. In a lawn 100 ft. square the circular basin of a fountain is 
40 ft. from each side. Draw a figure and find the area of the green- 
sward. 


10. A square is cut from a circle 12 in. in diameter. What is the 
size of each of the four equal segments cut from the circle ? 


11. In Exercise 10, what per cent of the circle was cut away ? 


12. A circular grass plot 2 rd. in diameter is surrounded by a 
walk 3 ft. wide- How many square feet in the walk ? 


Hint. Find the areas of the two circles — the grass plot, and the one includ- 
ing plot and walk. 


13. A circle 10 in. in diameter is cut from one 16 in. in diameter. 
What per cent of the large circle remains ? 


Oral MEASUREMENT OF SOLIDS 109 


1. Lines have one dimension; viz.: 


2. Surfaces have two dimensions; viz.: ——- and ——. 


3. Solids occupy space and have weight. They have three dimen- 
Slons ; V1z.: ; , and : 


4. Name the three common units of solid measure in the order of 
their size. 


5. ——cuin.=1 cu. ft.; —— cu. ft.=1 cu. yd.; —— cu. ft. = 
1 cord. 


6. State the method of finding the number of cubic feet in 20,000 
cu. in. 


7. 10 cu. ft. = cu. in. 9. 10 cords=~2 cu. ft. 


S720 Cieyd = 2icus tty 1020720 cur ft.==a cu. yd. 


Rectangular Solids 
What is a rectangle ? 


A solid bounded by sia rectangles is a rectangular solid. 


A solid bounded by six squares is a 
How many corners and edges has a cube ? 
Is a cube a rectangular solid? 

Describe an inch cube, or a cubic inch. 
Describe a cubic foot; a cubic yard. 


What is meant by a 2-ft. cube ? 


9. What is a9-in. cube? How many cubic 
inches in a 9-in. cube ? 


(See the figure.) Along one edge of a cube 9 
there is a row of x cu. in.; 9 such rows make 
a, tier of 9 x x cu. in. or y cu. in.; 9 such tiers 
contain 9 x y cu. in., or 729 cu. in. 


SraTEMENT. 9X9 xX9cu. in. =~ cu. in. 


110 RECTANGULAR SOLIDS Written 


Find the contents or volume of : — 


10. A 6-in. cube. 12. A 5-ft. cube. 14. A.10-yd. cube. 
11. An 8-in. cube. 13. A 12-ft. cube. 15. A 20-in. cube. 


16. Show that the volume of each cube is equal to as many units 
of measure as the product of the number of units in the edge taken 
as a factor three times. 

17. 5*’means 5x5x5. Since this is equal to the number of 
times 5 is taken as a factor to find the contents of a cube whose edge 
is five, 5%, or “5 to the third power,” is called “the cube of 5,” or 
“5 cubed.” 

TB Tah ox Ogle Ue” Cu ere) OF coals Eee 

19. What is one of the three equal factors of 64, or 1/64? 

20. »/216? 1728? W512? +/13312? +3729? +/27,000? 


Prisms 


1. Solids whose sides are all rectangles and whose bases are 
bounded by straight lines are prisms. 


2. Prisms are named from their bases: square, rectangular, tri- 
angular, hexagonal, etc. Name some objects that are square prisms; 
that are rectangular. 


3. Is a square prism also rectangular? What kind of prism is 
a cube ? 


Written MEASUREMENT OF PRISMS. PROBLEMS 111 


4. To find the contents of a rectangular prism whose dimensions 
are 4 in., 5 in., and 9 in. 


—_ 


Notice (a) the number of cubic inches in one row 
or square prism 1 in. by 1 in. by 9 in. 


(6) The number of such rows in one tier or layer 
4 in. wide. 


(c) The number of such layers in the prism, and 
explain the statement 5 x 4 x 9 cu. in. = @ cu. in. 


5. How many cubes may be put into a box 10 in. long, 8 in. wide, 
and 5 in. deep ? 


6. A trunk measures 3 ft. by 20 in. by 18 in. Find its cubical 
contents. Why multiply by 36 instead of 3? 


Find the contents of rectangular prisms of these dimensions : — 


LENGTH WIDTH HEIGHT LENGTH BREADTH DEPTH 
aeeLO- tte 10 ft. 8 ft. 10. 422 ft. 20:4: 13% ft. 
Sen Ley d. atts 9 in. 11. 124 yd. 10 ft. 16 in. 
gedit) 16h Lyd: Tome Oe tee tt ee Glin: 


13. How does the number of cubical units (cu. in., cu. ft., etc.) in 
any layer 1 unit thick compare with the number of units (sq. in., 
sq. ft., etc.) in the side of the layer ? 


14. If the base of a rectangular prism contains 30 sq. in., how 
many cubic inches in the bottom layer? If the prism is 10 in. high, © 
how many cubic inches in the prism ? 


STATEMENT. 10 x 30 cubic inches = z cubic inches. 


15. The floor of a cellar contains 36 sq. yd. If the cellar is 8 ft. 
deep, find its cubical contents. 


16. A square prism is 16in. wide and 4 ft. long. Find the volume. 


17. A 5-in. cube is cut from the corner of a 20-in. cube. What 
part remains ? 


112 MEASUREMENT OF WOOD Oral and Written 


1. Wood for fuel is generally sold in what lengths? In what 
form is it usually piled ? 


2. Give the dimensions of a cord of wood; a half cord; 4 of a 
cord, or a cord foot. 7 

3. What is the unit of measure used in measuring wood ? 

4. What kind of solid does a half cord represent ? 

5. Explain: 8x4x4 cu. ft.=~2 cu. ft. as applied to cord wood. 

6. A pile of 4-ft. wood, 4 ft. high and 8 ft. long, contains a cord. 
How many cords if 16 ft. long? 24 ft.? 321t.? 96 ft.? 

7. A pile of 4-ft. wood of the usual height must be how long to 
contain 10 cords? 12 cords? 25 cords? 


8. How many cords in a pile of 4-ft. wood 4 ft. high and 18 ft. 
long? Explain the following statement, and show what may be 


cancelled : — 
Ax a5 1S: Cun tt 


128 cu. ft. 


9. Bought a pile of 4-ft. wood 30 ft. long and 8 ft. high at $6 
per cord. Find the cost. 


= the no. of cords. 


4x8 x 30 


Aga, 
[age MAP a 


STATEMENT. 


In the statement, what represents the number of cubic feet? The 
number of cords? The cost of all? 


Find the value of piles of wood as follows : — 


LENGTH WIDTH HEIGHT PRICE LENGTH WIDTH HEIGHT #£PRICE 


10. 24ft. 4ft 6ft $4 13. 24 ft. 4ft. Tift. $3.50 
11 40 Thott. Sit.) ob 14. 20ft.  3ft 124 ft. $5.00 
12. 60ft. 10ft. 4ft. $6 15. 164ft. 44in. 22 ft. $4.25 


16. A pile of tan bark 8 ft. wide and 10 ft. high contains 200 
cords. How long is it? 


Oral and Written MEASUREMENT OF LUMBER 113 


1. Timber sawed for building purposes is lumber. What forms 
can you mention besides boards, planks, joists, and beams ? 


2. In measuring lumber no attention is paid to the thickness 
unless it exceeds an inch. A board 1 ft. square and an inch, or less, 
thick is called a board foot. 


3. A board 12 ft. long, 1 ft. wide, and 1 in. thick contains 12 board 
feet, or usually spoken of as 12 ft. What would a board 12 ft. long, 
10 in. wide and an inch thick contain ? 


4. A board 15 ft. long, 8 in. wide, and 3 in. thick contains how 
many feet ? 


Suecesstion. If the board were a foot wide it would contain 
it is but 2 of a foot wide it contains : 


feet. Since 


5. Ten 16-ft. boards averaging 9 in. in width contain how many 
feet? Explain the statement: 10 x $ x 16 board feet = x. 


6. A board 10 ft. long, 1 ft. wide, and 1 in. thick is equal to 
x board feet. If 14 in. thick it is equal to 14 x & board feet. 


7. Find the contents of a 3-in. plank 15 ft. long and 10 in. wide 
Explain: 3 x 2 x 15 board feet = a. 


8. How many feet of lumber in 12 joists, 16 ft. long, and 4 in. 
square ? 


9. Find the number of feet in 8 “3 x 4” joists each 12 ft. long. 
Note. A ‘3 x 4” joist is one 3 in. thick and 4 in. wide. 
Find the cats in board feet of lumber measuring as follows : — 
10. 6 boards, 16 ft. long, 14 in. thick, and 14 in. wide. 
11. Fifteen 3 x 4 joists, 18 ft. long. 
12. A stick of timber 18 ft. long and 12 in. square. 


13. A board 12 ft. long, 6 in. wide at one end and 10 in. at the 
other. 


Hint. Find the average width. 


114 THE SURFACES OF RECTANGULAR PRISMS Written 


1. How many surfaces has a rectangular prism ? 
2. What name is given to a rectangular prism with equal faces ? 


3. Find the entire surface of a 5-in. cube. 
Explain the statement: 6 x 5 x 5 sq. in. = @ sq. in. 


4. The entire surface of a cube is 150 sq. in. How long is it ? 


Find the entire surface of : — How long a cube has : — 
5. A 9-in cube. 8. An entire surface of 384 sq. in. ? 
6. A cube 10 in. long. 9. An entire surface of 600 sq. ft. ? 
7. A 16-in. cube. 10. An entire surface of 294 sq. in. ? 


11.. Compare the ends of a square prism with each other. 
12. Compare its four sides. 


13. Find the entire surface of a 
square prism 8 in. long and 3 in. wide. 
(What is the area of each square? 
How many? Of each rectangle? 
How many ?) 
14. Compare the opposite faces of 2 
any rectangular prism. 


15. Give the dimensions of each 
face in the figure at the right. What 4 
is its entire surface ? 


Find the entire surface of prisms : — 6 

16. 10 in. by 6 in. by 4 in. 

17. 12 ft. long, 9 ft. wide, 6 ft. high. 

18. 20 ft. long, 4 ft. wide, 8 ft. 
high. 

19. 16 x18 by 4; 20 by 1 by 1. 

20. 12 by 9 by 8; 23 by i by 16. 

21. 12 by 12 by 6; 2 by 3 by 74. 


Oral, Written THE VOLUME OF CYLINDERS hED 


1. A solid having ends (or bases) which are equal, parallel circles, 
and having uniform diameters is a cylinder. Mention some common 
objects that are cylinders. 


2. If the base of a prism is 6 sq. in., how many cubic inches in 
a section 1 in. thick? How many 
cubic inches in the prism if its height 
18.0 10.3 


3. Ifa cylinder is cut as in Fig. A B 
and arranged as in Fig. B, what does 
it nearly become ? 


4. If the circular end is the base, 
it has been changed into one nearly 
lke a rectangle. Has the area of the base changed in B? Has the 
length of the cylinder changed ? 


5. In B, if the base were a rectangle and its area known, how 
would its volume be found ? 


6. If the radius of A is 1 in., what is the area of its base or the 
base of B? If the length of Bis 8 in., what is the volume ? 


7. The volume that we have found by considering that the cylin- 
der is nearly a prism with an equal base and the same height, is the 
volume that is found by geometry to be the true one, viz. : — 


The volume of a cylinder is the same as that of a prism having 
a base of the same area and having the same height. 


8. Find the volume of a cylinder whose radius is 8 in. and whose 
height is 15 in. 

Explain the statement: (15 x 3.1416 x 8 x 8) cu. in. = acu. in. 

9. A cylindrical pail 6 in. in diameter inside and 12 in. deep 


contains how many cubic inches ? 
Explain the statement: (12 x 3.1416 x 3 x 3) cu. in. = weu. in, 


116 MEASUREMENT OF CYLINDERS Written 


10. A cylindrical tank is 10 ft. deep and 8 ft. in diameter. Find 
the contents. 


11. A gallon contains 251 cu.in. How many gallons will a cistern 
8 ft. deep and 4 ft. in diameter hold ? 


12. A well is 32 ft. deep and 5 ft.in diameter. Find the contents. 


13. To hold a gallon, a pail measuring 33 square inches on the 
bottom must be how deep ? 


To find the Surface of a Cylinder 
s. The rest of 


1. In form, the ends of a cylinder are equal 
the surface is convex surface. 
2. Suppose the diameter of a cylinder to be 4 in.; its circumfer- 
ence = 2, or 3.1416 x D. 

3. The circumference of a cylinder is 8 in.; its diameter is 
x, or ©. 
7 

4. A cylinder is 20 in. long and 4 in. in diameter. Find the 
area of its ends. ; 

5. Roll an oblong paper to form a cylin- 
der. Give the length and circumference 
of the cylinder thus made. . 


6. Unroll the paper and give the di- 
mensions of a rectangle equivalent to the 
convex surface of the cylinder. Explain 


the diagram at the right. es 


7. The convex surface is equal to CO x 
I square units, where C= circumference 
and £ = length. Why is this? 
8. A cylinder is 25 in. long, 4 in. in 
diameter. Its convex surface is x. Ex- 
plain: (3.1416 x 4) x 25 sq. in. = @ sq. in. 
9. A cylinder is 20 in. long, 5 in. in diameter. Find the entire 
surface, or the convex surface plus the surface of the ends. 


Oral MEASUREMENTS: REVIEW a ke Ey 


Nore. In oral work use #2 for 7. 
1. An old tree is 22 ft. round; how far is it through ? 


2. Give the convex surface of a lead pencil + in. in diameter and 
7 in. long. 


3. The sides that make the right angle of a triangle are each 
10 ft. What is the area ? 


4. It is 28 ft. across a pond. How far is it around it ? 
5. Which takes more room, a cord of wood or a 5-ft. cube ? 


6. 4a circle = a rectangle having the radius for one side and —— 
for the other. 


7. A 20-ft. log averages one square foot in the cross section. 
The cubic contents are x. 


8. How many cubic yards of earth will a bin hold that is 
pelts OTL. x29 fh.-? 


9. About how many cubic yards does your schoolroom contain? 


10. A horse tethered by a rope 10 yd. long can graze over how 
large an area? 


11. A cellar 18 ft. by 15 ft. by 74 ft. deep contains how many 
cubic yards? 
Written 


1. The largest possible circle is cut from a cardboard measuring 
16 by 24 in. What area of the cardboard remains ? 


2. What will it cost to cement the bottom of a circular cistern 
8 ft. in diameter at $ 2.50 per square yard ? 


3. The driving wheel of an engine is 6 ft. in diameter. How 
many revolutions does it make in going a mile if there is no slipping ? 


4, A large street roller is 5 ft. in diameter and 7 ft. long. How 
ereat an area does it cover in one revolution ? 


118 MISSING FACTOR FOUND Written 


1. o times: 6 = Aster ear 1 So: 
2. Multiplicand = 25; product = 400. How is the multiplier 
found ? 
3. 186+e#= 31. 
4. Dividend and quotient being given, how is the divisor found ? 
5. When the product and multipler are given, how is the multi- 
plicand found ? 
6. What is the area of a rectangle 12 ft. long and 64 ft. wide? 
7. A rectangle containing 108 sq. in. is 9 in. wide. How long is 
hii OR Oe SO aie LOS teqmians) | 
8. A lot 200 ft. long contains 24,000 sq. ft. How wide is it? 
9. A sidewalk 50 ft. long requires 50 sq. yd. of concrete. How 
wide is the walk ? 
10. One half an acre of land is taken for a new street 40 ft. wide. 
How long is the street ? 
11. The area of a triangle is 325 sq. in.; its base is 25 in. What 
is its altitude ? | 


12. The altitude of an isosceles triangle is 14 ft.; its area is 126 
sq. ft. What is its base? 


13. At 30 a board foot a mahogany board 1 in. thick and 12 ft. 
long cost $2.70. How wide was it? 


14. The area of a rhomboidal field is 12 A. Its length being 
20 rd., what is its altitude ? 

15. A square contains 400 sq. in. How long is it? 

16. The perimeter of a square is 1000 ft. Its area? 

17. A rectangular field 48 rd. wide contains 48 A. What is the 
other dimension? ‘The perimeter ? 

18. A rectangle is 3 times as long as wide and contains 108 sq. ft. 
What are its dimensions ? 


Suecrstion. Into how many squares can the rectangle be cut? What will 
be the size of each? The dimensions of each ? 


Written MEASUREMENTS 119 


CONTENTS OF A SoLIp AND Two Dimensions GIVEN To FIND 
THE THIRD 


df LS OPiS ho = POLO: 


2. I hired 15 men at $2.50 per day each. At the completion of 
the work I paid them in all $150. How many days did they work ? 


3. A box on my table holds 432 cu. in. It covers 72 sq. in. of 
the surface of the table. How high is the box ? 


4. The area of the floor of your schoolroom is 900 sq. ft. The 
room contains 10,800 cu. ft. How far is the ceiling from the floor ? 


5. A packing box is 48 in. long and 30 in. wide. How deep must 
it be to hold 10 cu. ft. ? 
10 x 1728 

48 x 30 
Explain the statement, and show a short solution. 

6. A closet 8 ft. high and 27 in. deep will contain 72 cu. ft. How 
wide is it? 

7. A pile of 198 ed. of 4-ft. wood covers 16 sq. rd. How long 
is it? How high is it? 

Explain the statement : — 


STATEMENT. = depth. 


Huong zy sli: 198 x 128 _ 
ig a Ata ionic 1652723 0 7 


8. A cylindrical oil tank holds 10 gal. Standing on the floor it 
covers 77 sq.in. How high must it be? 
9. A bookease holding 32 cu. ft. covers a wall space of 24 sq. ft. 
How far must it project into the room ? 
10. I have room in my stable for a grain bin 8 ft. by 4 ft. How 
deep shall I make it to have it hold 72 bu. ? 
11. A grindstone 4 ft. in diameter contains 6.2832 cu. ft. How 
thick is it? 
Explain the statement: 6.2832 + (2? x 3.1416) = a. 
12. In digging a trench 3 ft. wide and 44 ft. deep 330 cu. yd. of 
earth are removed. How long was the trench ? 


120 MISCELLANEOUS PROBLEMS Written 


1. I buy a corner lot 120 ft. by 50 ft. and use the earth obtained 
by digging a cellar 60 ft. by 30 ft. by 10 ft. to raise the grade, how 
many inches ? ; 


2. A circular standpipe 75 ft. high is 25 ft. in diameter. When 
2 full, how many gallons of water does it contain, reckoning 74 gal. 
to a cubic foot ? 


3. A speculator buys a field 600 ft. long and 500 ft. wide for 
$2500. He runs a 40-ft. street through the center in each direction 
at an expense of $425 for labor. He sells the land at 20 cents a 
square foot. How much does he make or lose ? 


4. At $3.75 per square yard what will it cost to pave # of a mile 
of street 81 ft. wide ? 


5. A reservoir supplies a town with 4,573,800 gallons of water 
daily. If its surface area is 7 acres, how much will the water be 
lowered in a week, providing 4 as much runs in as runs out? Call 
1 cu. ft. equal to 74 gal. 


6. From a lot of land 40 rd. square I sold 40 sq. rd. What is 
the remainder worth at $230 an acre ? 


7. The snow fall is 6 in. on the level. How many cubic feet rest 
on every acre of ground ? 


8. A watch chain cost $28. This is 7 of the cost of the watch. 
Find the cost of the watch. 


9. Wood is bought at $3.75 a cord. Transportation adds 15% 
to the cost, and storage 5% more. It is then sold at a profit of 20% 
on the total cost. What does it sell for ? 


10. A southern county contains 14,700 blacks. 334% of the 
population are white. What is the population of the county ? 


11. A schoolroom 12 ft. high, 30 ft. long, and 28 ft. wide contains 
40 pupils. How many square feet of floor space for each pupil ? 
- How many cubic feet of air for each one? 


Written MENSURATION: PRACTICAL PROBLEMS 121 


1. 64, 8, 44 are the dimensions of my coal bin in feet. Reckon. 
ing 90 lb. to the cubic foot, what will a bin full cost at $5 per ton ? 


2. Quincy granite weighs 165% pounds to the cubic foot. What 
is the weight of 6 pieces of curbing 8 inches thick, 2 feet wide, and 
half a rod long ? 


3. Find the cost of carpeting a 9-foot hallway 22 feet long with 
three-quarter carpeting at $0.874. Cut no strip, and allow 14 feet 
per seam for matching. 


4. How many tons of 15-inch ice may be cut to the acre, a cubic 
foot weighing 574 pounds? Apply your knowledge of cancellation. 


5. What is the capacity, in 42-gallon barrels, of a cylindrical 
oul tank 34 ft. in diameter, 22 feet long? Make a statement and 
cancel. 3 


6. What is the area of a sector of 120°, its radius being 24 inches ? 


7. A ball ground 375 feet long and 280 feet wide is inclosed by 
a tight board fence 8 feet high. What will the boards cost at $24 
per M? Add 10% for waste. 


8. Bought 12,000 long tons of coal at $4 and sold it at the 
same price per short ton. What did I gain ? 


9. What will it cost to polish the visible portions of a shaft of 
red granite 6 feet by 2 feet by 22 inches at 62¢ per square inch ? 


10. Draw a 6-inch square, a rectangle 9 inches by 4 inches, and 
one 3 inches by 12 inches. Compare areas and perimeters. What 
inference do you draw ? 


11. A schoolroom 82 feet by 30 feet is lighted by 6 windows, each 
containing 15 panes of glass 12 by 16 inches. The lighting surface 
of the room is what per cent of the floor surface ? 


12. My garden is 80 ft. by 100 ft. What will a concrete walk 
around the inside cost at 80¢ a square yard, the width of the walk 
being 35 feet ? 


2? MISCELLANEOUS PROBLEMS Written 


1. What decimal of a square prism becomes shavings when the 
largest possible cylinder is turned from it ? 


2. What number subtracted 88 times from 80,005 will leave 13 
as a remainder ? 


3. A railroad company fences 15 miles of its road at 732 cents a 
rod. What is the cost ? 


4. How many square feet of zinc will line a cubical cistern 5 ft. 
10 in. deep ? 


5. Bread sells for 10¢ with flour at $5.00. Flour goes up to 
$6.50. What should bread sell for on this basis ? 


6. In a city of 7200 school children there are 2720 cases of tardi- 
ness in a year, during which there are 400 sessions of the school. 
The average attendance is 6800. What is the rate of tardiness ? 


7. Find the cost of six 8 x 10 sills 18 ft. long at $24.74 per M. 


8. In a library every tenth book is a history. If there are 567 
other books in the library, how many volumes in all? 


9. A schoolroom measuring 32 ft. x 284 ft. x 13 ft. seats 49 
pupils. Each one needs 1800 cu. ft. of fresh air an hour. The 
room full would last the class x minutes. 


10. How many feet of wire will it take to fence a square field 
containing 625 sq. rd. if there are three rows of wire in the fence ? 


11. If I buy cloth at $1.20 per yard, how many yards must I 
sell at a gain of 20% to gain $20.40? 


12. How many yards of 3 yd. wide carpeting will be required to 
carpet a room 12 by 153 feet, allowing 5 inches to each strip for 
matching? The carpet selected was 85¢ per yard. 


13. A cubic foot of mahogany weighs 45 lb. What will be the 
weight of a piece of mahogany 5 in. thick, 20 in. wide, and 16 ft. 
long ? ; 


Oral MISCELLANEOUS EXERCISES 123 


1. What does the ga gas of a fraction show? Which is ° 
the larger unit, 7, or 7? Why? 


Pe.t WW hiehyis ee 22 or 24? Find this in a short way without 
changing to a like unit. 

3. What is the ratio of 2 to 2? To what unit did you change 
. both before you could compare them? Why ? 


4. Change 28 to 40ths. Explain the process. 


5. Explain the process of changing 82 to 28. 

6. Explain the process of changing 26 to 82. 

7. Compare 164 with 31. 11. $17 is 2 of $a. 

8. Add 34, 12, 28. 12. $6 is 3 of $x. 

9.. From 7} take 61. 13. 2 of 48 is 80% of «x. 
10. 16 x $81 = $z. | 14. 7:3L=11:2 


15. What per cent of a 2-foot cube is 3 cubic feet ? 


16. A miller takes 4 quarts toll from every bushel. What per 
cent is this ? 


17. I spent $27, or 30%, of my money. How many dollars had 
I remaining ? 


Hint. How many per cent remained ? Compare it with 30%. 
18. What is the rate of income on an $8000 house rented at $40 
per month ? 


19. If wages are increased 10%, what will men now receive who 
received $1.50 before ? 


20. Men who now receive $2.75 after a 10% raise in wages 
received what before the raise ? 


21. What is 31% of 500? 51% of 600? 

22. $2 is what per cent of $800? Of $80? Of $8? 

23. 0.42 + 70 = what? 25. 0.006 + 0.12 = what ? 
24. 4.2 + 700 = what? 26. 0.06 + 0.012 = what ? 


124. MISCELLANEOUS EXERCISES Written 


1. A lot of land cost $2800. This was y% of the cost of a house. 
The house cost @ dollars. 


2. How many bags will be required for 1000 bushels of wheat, if 
each bag holds 2;°, bushels ? 


3. The snowfall is 5 inches on the level. How many cubic feet 
rest on 24 A. of ground ? 


4. The races start at precisely 2.15 p.m. The winner returns to 
the starting point at 5.36 pw. He has averaged 32 miles an hour. 
How far did he travel ? 


5. Give the day and hour when exactly 3 of the month of March 
has passed. 


6. 2800 mill operatives earn on the average $1.68 a day. If 
their wages are reduced 10%, what will the weekly saving to the 
company be? , 


7. Inacity with an average attendance of 10,000 in the public 
schools, which keep 360 sessions during the year, how many tardi- 
nesses would there have been to each thousand pupils if the whole 
number of tardinesses for the year had been 3600 ? 


8. The interest on a mortgage is payable semiannually at 51%. 
The face of the mortgage is $2300. How large a check should be 
remitted to pay the interest as it falls due ? 


9. What will it cost to bronze a 2-foot cube at 14 ga square inch ? 


10. Hay is bought at $12 aton. Transportation adds 15% to 
the cost, and storage 5% more. It is then sold at a profit of 20%. 
What does it sell for ? 


11. I can buy alcohol for $2.75. If I import it for school use, I 
can buy it for 90 ¢. Thisisa saving of 7%. 


12. The number of children of school age in a certain city is 
14,769. This is 331% of the whole population. How many not 
school age? Work a short way. 


Oral MISCELLANEOUS EXERCISES 125 


1. A pint of meal is put into a peck of flour. What per cent of 
the mixture is meal? 


2. How many bullets, each weighing } oz., can be molded from 
2 lb. of lead ? 


3. May was sent to the store for 4 pk. of apples. What did she 
pay, for them, if they were $3.20 a bushel ? 


How many pens can I buy for $2, if I buy 2 for a cent ? 
What numbers between 30 and 50 are perfect squares ? 
What is the cost of 12 oranges at 3 for 5 cents? 


4% of a number is 50. What is the number ? 


+02. 8 


8. The difference between + and 4+ of my money is $30. How 
much have I? 


9. Which is the better bargain, bananas at 20¢ a dozen or 16 for 
a quarter ? : 


10. A mason works 8 hr. for $3.00, and a carpenter 10 hr. for 
$3.50. How much more does one earn than the other in 100 hr. ? 


11. What is 7 months’ rent of a telephone at $50 a year ? 


12. How long will it take a girl to earn $5, if she works half the 
time for 18¢ and half the time for 12¢ an hour? 


13. Three boys who are 10, 12, and 14 years old respectively are 
to share $54 in proportion to their ages. What is the share of 
each ? 


14. Two men agree to cut lumber for $200. One, with 3 men, 
works 5 days, and the other, with 4 men, works 6 days. How much 
of the money should each receive ? 


15. Paid $21 for insuring my house for 5 yr., at 3%. What is it 
worth, if it is insured for 7 of its value? 


16. A teacher’s salary is $60 a month, If it is raised 84%, what 
does she then receive ? 


126 MISCELLANEOUS EXERCISES Written 


1. Find the sum of :— 


2496 2. Find the total cost of the following: 33 lb. of but- 
3948 ter at 28 cents a pound, 9 lb. 9 oz. ham at 16 cents a 


eee pound, 8 lb. 10 oz. cheese at 24 cents a pound. 
9625 3. A man sold 3 of his farm for $3900. What was 4 
a of the farm worth at the same rate ? 

9) . 
6498 4. A builder bought 6500 brick at $7.50 per thousand, 


5936 12,200 ft. of lumber at $16.50 per thousand feet, and 
4073 975 lb. nails at $3.80 per hundred pounds. What was 


Bee the amount of his entire bill? ) 
5678 5. What will it cost to carpet a room 54 ft. long and 


6935 30 ft. wide with Brussels carpet 2 of a yard wide at $1.24 


ee per yard, making no allowance for matching ? 
4678 6. A man bought a house for $2500 and sold it for 


3979 $1875. What per cent of the cost did he lose ? 
8462 


9879 7. What is the interest of $320, at 6 per cent for 2 yr. 
6432 10 mo. 12 da. ? 
te 8. A merchant sold goods for $240, thereby losing 4 


9346 of the cost. For what amount should he have sold them 

ange to gain 15% ? 

9. During the winter of 1902 and 1903 a ton of coal lasted a 
family 14 days, average time. What did the coal cost at $5.25 a ton 
from Oct. 1 until March 31, inclusive? What would the coal cost 
for the same length of time at an increase of $4.25 a ton ? 

10. A house which cost $9600 rents for $48 amonth. This is 
a% income from the investment, if the yearly expenses amount 
to $96. 

11. A flour merchant sold 240 bbl. of flour for $1582, which was 
4 less than he paid for it. What was the whole cost? The cost per 
barrel ? 

12. Ifa cubic foot of granite weighs 165 lb., what will a 6-in. cube 
weigh ? 


Oral MISCELLANEOUS EXERCISES 127 


1. How many yards of ingrain carpet will be needed for a room 
Date Oya Loot. 


2. A building lot contains 5380 sq. ft. and is 100 ft. long. How 
Wide is it? 

3. Divide 0.6 by 0.015. 4. 4x W256 =o. 

5. A house bought for $3200 sold for $3000. What per cent 
of the cost was lost ? 

6. What part of anything is 124% of it? If 121% of my money 
is $25, how much have I ? 


7. What will pay a note of $500 that has been running 2 of a 
year at 9% interest ? 


8. Goods marked at $1.50 per yard were sold at 331% discount. 
What did 5 yards cost ? 


9. Bought 3 for 4¢ and sold 2 for 3%. Did I gain or lose and 
how much ? 


10. Bought for $10 and sold for $2.50. What per cent of the 
cost was lost ? 


11. My weight increased from 150 lb. to 175 lb. What was the 
per cent of increase ? 
12. Read as per cents : — 


1 1 Tiegh SOR Vg EY fa 
NG We a GER YA ray) aoe 


“ 
Ae 
“ 


13. Read in largest units : — 
123%; 18$%, 314%, 813%, 435%, 564%, 833%. 
14. It is 160 rods around a square field. How many acres does it 
contain ? 
15. At15¢ a yard, picture molding for a room 12 ft. by 18 ft. will 
cost how much ? . 


16. Paid $2.40 for 15 lb. of meat, 20% of which was bone. What 
did the meat really cost per pound ? 


128 MISCELLANEOUS EXERCISES Written 


1. If 22 yd. are bought for $23.10, what is paid for 15% yd. at 
the same rate ? 


2. 67.24 x 82% — 67.24% + 82 = what? 


3. Ina flag 174 ft. long and 2 as wide, how many square yards 
of bunting, not allowing for seams ? 


4. How many cubic yards of earth will be thrown out in digging 
a cellar 54 ft. long, 2 rd. wide, and 9 ft.-deep ? 


5. What per cent of its daily trip has the long hand of a clock 
accomplished at 3 p.m. ? 


6. I insure my house for $2400. How much premium do I pay, 
the rate being 3% ? 


7. What is the interest of $400 for 3 yr. 3 mo. 20 da. at 6% ? 


8. If I buy flour at 3; cents a pound and sell at 4,5 cents a 
pound, what part of the cost is the gain ? 


9. What per cent of a floor 16 ft. square is covered by a rug 12 ft. 
square ? 


10. A man sold 374% of his business for $3900. What was ¢ of 
it worth at that rate ? 


11. Aman built a double house at a cost of $4500 on a lot valued 
at $1500. If he receives $30 a month from each tenant, and pays 
$100 for taxes and $20 for repairs, etc., what part of his investment 
will his net income be ? 


12. If flour sold for $4.25 a barrel gains 61%, at what price should 
it be sold to gain 15% ? 


13. If 4 of 3 of a ship is worth $8600, what is 2 of it worth ? 
14. Change 0.096 to a common fraction whose denominator is 875, 
15. How do sixths and twenty-sevenths compare in size ? 


16. How many 63ds in 33? 


TABLES OF MEASURES 


129 


[FOR REFERENCE | 


Counting 


12 things = 1 dozen (doz.) 

12 dozen = 1 gross (gro. ) 

12 gross = 1 great gross (G. gr.) 
20 things = 1 score 


24 sheets (paper) = 1 quire 
20 quires or 
\ = 1 ream 


480 sheets 
Time 


60 seconds (sec.) = 1 minute (min.) 


60 minutes = 1 hour (hr. } 
24 hours = 1 day (da.) 

7 days = 1 week (wk.) 
2 weeks = 1 fortnight 


30 (81, 28, 29) days = 1 month (mo.) 


3 months or mee ae 
13 weeks } cae ee a 
12 months or _ 1 year (yr.) 
365 days } ~ (common) 
365 da, 5 hr. 48) _ { 1 true or solar 
min. 49.7 sec. } * year 
366 days = 1 leap year 
10 years = 1 decade 
100 years = 1 century (C.) 
Value 
U.S. Money 
10 mills = 1 ct. (ct., c., or %) 
10 cents = 1 dime (di.) 
100 cents or 
meet \ = 1 dollar ($) 
10 dollars = 1 eagle 


Canadian Money 
100 cents = 1 dollar = $1 


English Money 
12 pence (d.)=1 shilling (s.)=$0.248+ 
20 shillings =1 pound (£)=$4.8665 
French Money 
100 centimes = 1 franc (fr.) = $0.1938 


German Money 
100 pfennigs = 1 mark (M.) = $0,238 


Capacity 
Liquid Measures 
4 gills (gi.) = 1 pint (pt.} 
2 pints = 1 quart (qt.) 
4 quarts = 1 gallon (gal.) 


TPegaiton, | 5281 tu..in. 


Dry Measures 
(For grain, fruit, ete.) 


2 pints = 1 quart 

8 quarts = 1 peck (pk.) 

4 pecks = 1 bushel (bu.) 
10 pecks 


21 bushels \ = 1 barrel (bbl.) 


1 bushel = 9150.42 cu. in, 


Weight 
Avotrdupois Weight 


16 ounces (0z. ) = 1 pound (1b.) 


1 hundred- 
pe oats rf eee (cwt. ) 
2000 pounds or _ f thtone CD 
20 paar eet { (short) 
2240 pounds = 1 long ton 


130 


*60 pounds = 1 bushel { PRON 
potatoes 
Sh ac Nt Sih corn or rye 
H Soe te aril Be ea oats 
1 OGiee tS eee barre! flour 
BOO GSW nie pe beef or pork 


* In most States 


Troy Weight 


(For precious metals, jewels, etc.) 


. = 1 pennyweight 
24 grains { 
8 (pwt.) 
20 pennyweights = 1 ounce 
12 ounces = 1 pound 


4371 grains = 1 ounce 


7000 1 pond vF 
480 (ee 1 OUnes Tro 
5760 ‘ =1 pound y 
Apothecaries’ Weight 
20 grains = 1 scruple (sc. or D) 


3 scruples = 1 dram (dr. or 3) 
8drams = 1 ounce (oz. or 3) 


12 ounces 
5760 grains \ = 1 pound (lb. or tb) 


Length 
12 inches (in.) = 1 foot (ft. ) 
3 feet = 1 yard (yd.) 
164 feet or 
se \ =\1 rod (rd.) 
320 rods 
5280 feet = 1 mile (mi.) 


63,360 inches 


4 inches = 1 hand 


TABLES OF MEASURES 


6 feet = 1 fathom 

6086.7 feet or 1 knot 
1.15 + com- \ 1 nautical mile’ 
mon miles 1 geographic mile 

3 knots = 1 league 


Circular Measure 
60 seconds (/’) = 1 minute (') 
60 minutes = Pdegrearts) 

360 degrees = 1 circumference 
694 miles or 1° of latitude; or 
60 ccosraphic} = | 1° of longitude 

miles on the equator 


Surface or Square 


144 square inches \ nN { 1 square foot 


(sq. in.) (sq. ft.) 
1 square yard 
9 square feet = { 

: (sq. yd.) 
304 square yards \ io Ne square rod 
2721 square feet i. (sq. rd.) 
160 square rods lis 
43,560 square feet J ace eee ; 
BAN eres ia { 1 square mile 

(sq. mi.) 
1 mile square = 1 section 
36 square miles = 1 township 
1 square 
100 square feet = (in roofs, 
floors, etc.) 


Solid or Cubic 


1728 cubic inches \ ‘ig te cubic foot 


(cu. in.) (cu, ft.) 
27 cubic feet = { 1 fas 


Wood Measures 
16 cubic feet. = 1 cord foot (cd. ft.) 


128 cubic feet 
8 cord feet jf pcord (oe) 


THE SOUTHWORTH-STONE ARITHMETIC 
THIRD BOOK 


PART II 
PERCENTAGE 
Computing by Hundredths 


1. One hundred is the common standard of comparison. For 
example, the merchant may gain $10 on every $100 invested, or 
10 per cent (10%). The rate of interest may be 6%, or $6 on 
every $100 used. 

2. What is meant by saying: — 

12% of the grain spoiled ? 
384% of the month was stormy ? 
14% of the pupils were absent ? 

38. The phrase per cent (the short form of per centum) means 
hundredths, or by the hundred. 

4. 25% of 400 is 25 times one of the 100 equal parts of 400, 
or 


5. 100 is what part of 400? 1L= 4), or %. 


6. If 25% of a number is 100, what is the whole number ? 


Hint. All of the number or 43° of it =—— x +45 of it, or —— x 100 = ——.. 
It is seen in the preceding examples that there are three general 
classes of problems in percentage, viz. : — 
I. The whole given to find a part. 
II. A part given to find its relation to the whole. 


III. A part given and its relation to the whole to find the whole. 
151 


182 PERCENTAGE Oral 


The Whole given to find a Part 


Find : — 

1. 121% of 96 lb. 6. 331% of 24 hr. 

2. 20% of 90 miles. 7. 30% of 200 acres. 
3. 50% of 2000 lb. 8. 14% of 300 pupils. 
4. 25% of $ 60. 9. 25% of 1200 votes. 
5. 75% of 400 yd. 10. 6% of $3000. 


A Part given to find its Relation to the Whole 
1. Compare 2 and 4; thus, 2 is 4 or 50% of 4; 4 is 2 times or 
200% of 2. 
2. Compare 3 and 6; 2 and 8; 3 and 12. 
. 5 is what part of 20? What % of it? 
%, of 48; $24 is what part of $36? What %? 
. 12 ounces is what part of a pound? What % ? 


3 
4. 161s 4, or 
5 
6 


. 800 lb. is what part of a ton? How many 100ths of a ton, 

or % of it? ! 
7. 16=what % of 40? 9. 96 = «7% of 144. 
8. 48= what % of 64? 10. 35=%% of 105. 


A Part given and its Relation to the Whole to find the Whole 
1. 4 of my age is 16 years. How old am I? 
2. 50%, or 4, of my money is $80. How much have I? 
3. ¢ of the price was $36. 4 of the price was 1 of $36; and 4, 
or the whole price, was x $ AOL 
4. 6% of my salary is $72. 1% of my salary is $——, and my 
whole salary is 


5. A whole flock is how many times 25% of it? If 25% ofa 
flock is 40, the whole flock is x 40, or 


6. What is the relation of all of anything to 50% of it? To025% 
of it? To12}% of it? To 334% of it? To 662% of it? 


Oral 


Which are decimals ? 


it ? 


PER CENT AS EQUIVALENT TO FRACTIONS 


25 = 0.256=4. Which are fractio 


Which is most anil used ? 


1. 25 per cent = 25% = 


133 


Mise 


2. 123% =4 of 25%=4 of f=1. 

38. 61% =1 of %=4 of gh Ss 

4. 371% = x 124% =——_ xl= 

5. 50% =——;, 624% =50%+ %=t+ =—. 

6. 15% =3 x I 3 874% = 15% + — = 3 + — = —_. 
7. 84% = what fraction ? 12. 143 =F = 1. 
8. 163% = —— x 81% = what? 13. 284% = what? 
9. 412%= x 84% = — 14. 428% = what? 
10. 584% =50%+ = —— 15. 574% = what? 
11. 834% =75%+ = —. 16. 712% = what? 
17. 912% =100% — 81% =1-—7,=—_. 

18. 933% =100% — «2% =—— 

19. Find 142% of 280 feet. hn 0 a then 142% of 280 feet = 


+-of 280 feet = what ? 
20. What is 581% of $24? 55 of $24= $2. 
21. If 162%, or 1, of my money is $30, how much have I? 


22. What is the relation of all, or 100% of anything, to 374% of 


If 371% of it is 6 ft., what is all, or 100% of the length? 


The following fractions are used so often that we ought to know at 


sight that : — 
$= 50%. = $= 40%. = 124. oy = 5M. 
$=331%. $=60%. $= 37%. B=4%. 
$= 663%. 4=80%. $=62%. dy =3h%. 
$= 25%. $= 162%. f=8T%. B= 2%. 
$=75%. $=834%. ty =8h%. Hy = 2%. 
$= 20%. = $= 149%. te = 68%. = = OM. 
23. What is 624% (or 8) of 40? Of 64? Of 100? 


24. Subtract each per cent in the table from 100%. 


134. PERCENTAGE Oral 


Determine whether you are to find all, a part, or the per cent that a 
part is of the whole, and then find : — 


1. 623% of 72. 5. 121% of 96. 

2. 124% of a gross. 6. 142% of 70. 

3. 142% of 30. 7. 50% of $37.50. 

4. 331% of a sq. yd. 8. 25% of $48.60. 

9. 7 is what part of 28? What per cent of 28? What part of 


49? What per cent ? 


10. 13 doz. are 334% of doz. 14. 161s what % of 20? 


1126 qt. are 621% of gal. 15. 15 is what % of 60? 
12. 30 pk. are 662% of bu. 16. 20 is what % of 60? 
13. $17 are 20% of $—_. 17. 75 is what % of 300? 


18. 621% of $49.60 was 4 of A’s indebtedness. He paid 4 of the 
amount. What is the balance ? 

19. A teacher pays $6 per week for board and room, which is 
40% of her salary. What is her salary for a school year of 40 weeks ? 


20. I pay for rent $750 a year, which is 331% of my income. 
What do I receive annually ? 


21. A mechanic receiving $72 a month spent $60. What per 
cent did he save ? 7 | : 

22. An agent collected a bill of $6000, and received $1500 com- 
mission. What was the rate per cent ? 


23. A farmer sold 64 bu. of apples, 874% of which were of the 
first quality. How many were of the second quality ? 


24. Bought 12 doz. buckets at 25¢ each. I wish to make 331% 
profit. How much must the marked price be per dozen ? 

25. A merchant having $2000 paid $500 for a team. What per 
cent remained ? 


26. A grocer received 60 bbl. of flour, and sold 12 of them the day 
they arrived. What per cent had he still ? 


Oral PERCENTAGE 135 


What is given? What are you to find ? 
1. 45 is 834% of ? 3. 5 oz. are 121% of lb. 
2. 3is 2% of ? 4. 6 dimes are 60% of $—_. 
5. What per cent of a bushel is 4 quarts ? 

6. What per cent of $120 is $10? 


7. Dick caught 80 fish in a week, and Tom caught 16. What per 
cent of the whole did Tom catch ? 


8. Paid $75 for a watch, and sold it for $50. I lost #%. 


9. A mechanic worked for $3.50 per day. His helper received 
142% of $3.50 per day. What is the sum of their wages ? 

10. A boy earned $1.50 in a week, 60% of that amount the next 

week, and 662% of it the third. How much did he receive in all ? 


11. A certain locomotive ran 990 miles without repairs. Another 
ran 662% of this distance farther. How far did the second one go? 


12. Find 50% of $6200. 15. Find 1% of 6200. 
13. Find 25% of $5200. 16. Find 1% of 5200. 
14. Find 75% of $1600. 17. Find 3% of 1600. 


What is the difference between : — 
18. 162% of 480 acres of land, and 1 of 240 acres ? 
19. 142% of $105 and 4 of $105? 


20. A trader sold a horse for $175, which was 873% of its cost. 
How much did he gain or lose by the transaction ? 


21. A number increased by 20% of itself is 72. What is it? 
22. One dollar and twenty cents is 20% of what number ? 
23. A merchant sold goods for $54 and lost 10%. The cost? 


24. C wrote a check for $40, which was 31% of his bank balance. 
How much remained after the check was paid ? 


25. A man’s expenses are $7.50 per week, which is 81% of his 
income from a small farm. What are the profits from the farm ? 


136 PERCENTAGE Written 


1. A farm that cost $5400 was sold for 75% of its value. What 


was the selling price ? B 
$ 5400 
AY 0.75 
3 gen $ 270.00 
75% nae $ 5400 = $4050. 3780.0 
$ 4050.00 


Of the two methods, A and B, which seems preferable? Why? 
When can method A be used to advantage ? 
When will it be better to use method B? 


5. 434% of my crop of 3290 bushels of wheat has been sold. 
How many bushels did I sell? (Which method? Why ?) 


6. I paid $3400 for a house and sold it for 87% of what I paid. 
What did I get for it? (Which method? Why ?) 

7. Of the $2700 paid for an estate, 121% was in cash and the 
remainder in notes. What was the cash payment? (Method ?) 


8. Of 12,650 bushels of grain, 34% was in corn, 28% in oats, and 
the remainder in wheat. There were a bu. of corn, y bu. of oats, 
and z bu. of wheat. Explain the statement : — 


[100 % — (34% + 28%)] x 12,650 bu. =z bu. 


ee pe 


How much is : — Find a discount of : — 

9. 25% of 3742 tons ? 12. 15% on 61 yards at $2.50. 
10. 74% of 784 miles ? 13. 374% on a $558 piano. 
11. 162% of 5733 acres ? 14. 183% on 42 tons at $6.50. 
15. Compare ? of $400 with 3% of it. 

16. Read: 0.003; 2%; nae Explain : A 


17. What is Z of $64,000? 18. Find 2% of $64,000. 


19. My property is assessed for $24,800. Tax rate 18%. My 
tax ? 


Written PERCENTAGE 137 


1. I bought a house for $3600, and sold it at a gain of $540. 
What % did I gain? 


0.15 = 15% EXPLANATION. Comparing the gain with the 
360) 54 00 cost, the ratio of the gain to the cost = $4. This 
fraction eXpressed as a decimal is 0.15, or 15%. 


36.00 Observe that the % one number is of another is their 
18.00 ratio expressed as hundredths. 
18.00 


2. 6035 persons bought tickets toa fair. This was what per cent 
of the 8500 that attended ? 

3. 625 pupils belong in the Lincoln school. 600 of them are 
present, or «% of the whole. 


4. 37%, or 11,100 tons, of an ice crop remained unsold. There 
must have been # tons in the whole crop. 


5. The cargo of the Sea Hing was valued at $38,475. The value 
of the cotton was 162% of the whole, that of the sugar 374%. The 
miscellaneous part of the cargo was valued at x dollars, or y% of the 
whole. Take the shortest method. 

6. I sold my bicycle for $17. It cost me $25. I must have 
lost what: per cent of the cost ? 


7. If I had lost but 15%, I should have sold it for what ? 
8. 192 pages of a book of 432 pages are illustrated. That is 
what % of the whole ? 


9. If a retail dealer has habilities amounting to $1125, and owns 
property amounting to $675, what per cent will he be able to pay his 
creditors ? 

10. A man owned $175,000 worth of real estate in a certain city, 
but he has recently sold $145,000 worth of it. What per cent of it 
does he still own ? 


11. A city inereases 24% in 10 years; that is from 37,860 popu- 
lation to a. 


138 PERCENTAGE Written 


1. I gained 15%, or $540, when I sold my house. Find the cost. 


aA x 8 54) = $ 3600. 
Expianation. The whole cost is 492 of 15% of 
O00 it, or the ratio of 100% of. et cost to 15% of it is 19 
or 15)$ 54000 Hence the house cost 49° x $540. Jf it is not easy 
45 to cancel the terms, the aiisiOn may be performed in — 
90 the usual way. 
90_ 
00 
2. $260.01 is 27% of $—. 5. $1406.25 is 45% of $—_. 
3. $533.40 is 84% of $—. 6. 134.64 qt. = 51% of x gal. 
4. $368.93 is 79% of $ —_. 7. 113.49 ft. = 39% of a yd. 


8. The Indian population, according to the census of 1900, was 
about 145,000, which is only 58% of what it was in census of 1890. 
What was it in 1890, and what was the decrease, in round numbers ? 

9. There are 2844 school children ina certain city. This is as 
of the population. What is the population ? 

10. A man sold 20% of his interest in a mill for $38,000. Ashe 
owned 20% of the mill, the mill was worth $a. 

11. About 50,000,000 sq. mi. (or 25%) of the earth’s surface is 
land and the remainder is water. What is the area of the water ? 

12. Ina certain school 19 pupils are post graduates, 391 are regu- 
lar students, and the remaining 374% are students taking special 
courses. How many are enrolled ? 

13. A man saved $12,597 in ten years, and this amount was 5% 
of his whole property. What was he worth at the end of that time? 

14. A Western ranchman sent 381 cattle to the Chicago market, 
which was 60% of the number he sent to the Eastern dealers. He 
found he had sold in all 4 of his drove. How many had he at first ? 

15. A man owed $470 in 1900, which was 40% of what he owed 
in 1898. How much did he owe in 1898 ? 


Oral and Written PERCENTAGE 1389 


1. Which is more profitable, a gain of 3 per dozen, 5 per score, 
25 per cent, or 36 per gross? Why? 

2. Compare 2 of something with 2% of it. 

3. Six wrong out of 24 problems solved is @ wrong out of a 
hundred, or 7%. 


4. The Clevelands won 7 games in their series with the Pittsburg 
Club, the Pittsburgs won 4, and the one game was a tie. The win- 
ner’s per cent was z. 


5. Thirty-six hits in 80 times is a batting average of 7%. 


6. The center fielder has 80 chances, and makes 4 errors. His 
fielding average is 7%. 


7. The crew pulled 36 strokes to the minute at starting, but fell 
off to 30 at the finish. This was a loss of what per cent ? 


8. 9. 10. 
2% of 600 = 2. £% of 800 = a. xe = 874% of 128. 
2% of x = 2. $% of 2 = 12. “9% of 144 = 120. 
x% of 1200 = 8. x% of 200 = t. 834% bad and #% good. 
ie i ~eaky 
25% of 52? 19 is %% 57. 25 is 4% of a. 
35% of 400 ? 70 is w% 2100. 280 is 14% of a. 
81% of 22°? 162 is x% 662. 8 is $% of a. 


14. I paid 2% commission to my agent for selling a farm for 
$1250. How much money did he have left to send me? 


15. 21% was paid a collector who earned $22.50 a month in this 
way. What were his annual collections ? 


16. Of a farm of 320 acres 108 acres are given to wheat, 96 acres 
to oats, and the remainder to corn. What per cent of the farm are 
the cornfields ? 


17. The frost destroyed 27 per cent of a crop of oranges, and 
only $1660 was realized. What was the loss? 


140 


PERCENTAGE: TABLE FOR PRACTICE 


The number of hundredths, or per cent, is sometimes called the 
The number of which a part is to be found is called the base, 
and the part of the base required, when found, is called. the percent- 
For brevity these terms are used in the following table: — 


rate. 


age. 


Find the value of x. 


a 


ovo F§ FY FY KF FF FP SYP EF ES 
oo mo nrt Oo OM Fr wo HO K OC 


Rate % 


Oral WRITTEN 
Base Percentage Percentage Base Rate % 
$9.30 x 1 32,45 mi. 2674 mi, x 
x 125 tons 2 170.40 ay 17% 
75 yd. 183 yd. 3 36 yr. 130 yr. x 
x 57 4 184 A. by 454 
9000 mi. o 5 4857.6 ft. 5280 ft. cy 
$0.50 $ 0.314 6 $5.76 ie 4 
x 14 da. 7 $ 5400 $ 9600 i 
14 tons ~ 8 x 1500 ed. 15 
160- 1062 9 | 204 sq. ft. | 5200 sq. ft. | a 
x 15 sq. mi. | 10 6500 T. % 834 
725 x 11 143 da. 365 da. x 
a century 8 mo. 12 | $13,651.56 $ 75,842 x 
608 bu. © 13 5 36 x 
x 18 bales 14 84 x z 
75 rd, 61 rd. 15 a 314 162 
$ 12,000 x 16 328.8, a 94 
x 35 cords 17 $ 349.06 $ 9006 x 
726 gal. 605 gal 18 $18 x 4 
$120,000 x 19 13 $8100 fs 
x 34 Ib 20. x 3 3 


Written PERCENTAGE: BUSINESS PROBLEMS 141 


1. Sold a house that cost $5000 at a profit of 80%. Proceeds 
of sale? 


2. A merchant’s sales for January amounted to $28,000, but 
12% was lost in bad debts. The net proceeds of the sales for the 
month were w dollars. 


3. Gained $12, or 20% in selling a Century Dictionary. It 
cost me w dollars, and I sold it for y dollars. — 


4. A sewing machine cost me $24. I sold it for $32. I gained 
x . | 
32 — 24 
Explain the statement: Ea x. 


Nore. The gain or loss is always reckoned on the cost. 


5. A conductor’s wages are $72 amonth. They are reduced to 
$60. This is a cut down of #%. 
72 —60 - 

A = x%p : 

12 


6. Cost, $8000; selling price, $6000; loss per cent, a. 


Explain the equation : 


7. Cost, $6000; selling price, $8000; gain per cent, a. 

8. Which is more profitable, to buy cloth for $5 and sell it for 
$9.50, or to buy for $4, and to sell it for $4.80 ? 

9. Gas is reduced from $2 to $1.60 per 1000 cu. ft. How much 
do I save on $45 worth of gas ? : 


10. Last winter my coal cost me $6 a ton. This winter, I pay 
$8. This is an increase of what per cent? 


11. A man sold two city lots for $5600 each. On one he gained 
1429, on the other he lost 124%. Find the loss or gain. 


12. Bought silk at $1.75 a yard. I marked it to sell at a gain of 
20%, but sold it at 334% less than the marked price. What per - 
cent did I gain or lose ? 


13. 160 is 10% more than what ? 


142 PERCENTAGE: PROBLEMS Written 


1. Bought wood at $4 a cord and sold it at a gain of 20%. 
What did I sell it for ? 
(4) $44 20% of $4=a. (b) 120% of $4=2a. 
-. Explain the two statements. Which suggests the shorter solution ? 
2. Sold a typewriting machine that cost me $80 at a loss of 10%. 
What did I receive for it? 
_ (a) $80 —10% of $80=%. (6) 90% of $80=—z2. 
Explain the two statements. Which is preferable? 


3. Bought a house for $4800 and sold it at a gain of 16%. Find 
the selling price. Which method ? 


4. Sold a dwelling house for $7500 at a profit of 25%. It cost 
me « dollars. 


5. An epidemic decimated a southern village, leaving it with 
but 639 inhabitants. How many died? (What does decimate 
mean ?) 


6. A farmer who owned 390 acres increased his farm 30% within 
2 years. How much did he own at first ? 


7. A speculator lost $3000 or 6% of his property. What was 
it then worth ? 


8. A sold a yacht for $800 at a loss of 60%. Required its cost. 


9. A piano that cost $450 was sold for $292.50. What was the 
per cent of loss ? 


10. Some people feel that if the seller reduces his price, they are 
buying at a bargain. I wish to take advantage of their weakness by 
marking a certain line of goods which cost me $1.20 a yard so that 
I can fall 10% from the marked price and yet make a profit of aU 
_ What is the marked price ? 


11. How shall I mark goods that cost me $2 so that I can sell at 
a discount of 20% and yet make 40% on the purchase ? 


At Sight REVIEW 143 
1. In $3 what per cent is the numerator of the denominator ? 
In 2? 
2. What is ;4, of a rod in feet? In inches ? 


3. 231 cubic inches=1 gallon. Separate 231 into its prime 
factors. Give the dimensions of a tin pan that will hold a gallon. 


4. What part of a year are the longest three months ? 
5. What is 4% of 21,000? 


6. 331% of 60% of 4 of the money remained. What part did 
the thieves take ? 


7. My property is assessed for $2500. The rate of taxation is 
21%. What is my tax ? 


8. What per cent of the surface of a 4-inch cube is on five 
sides of it? 


9. Bought thread for 4 cents a spool and gained 300%. It sold 
for « cents. | 


10. 81% of a yard = 7% of a foot. 

11. Three sides of a square = 7% of its perimeter. 
12. «% of the day has passed at 9 P.M. 

13. (£4+30% + 3) of 64 is 25% of a. 

14. 16 is 2 of x and 2% of y. 


15. Gave $24 to James and $30 to Lucy. Lucy had #% more 
than James, and he had y% less than Lucy. 


16. Paid the price of a pound for 14 ounces. I thus lost 7%. 
17. V9 =2% of V144. 


18. In aseries of ball games the Alphas won 40% and the Omegas 
50%. Two games were drawn. How many were played ? 


19. 4a mile is what per cent of two leagues ? 


144 PERCENTAGE: BUSINESS PROBLEMS Oral, Written 


1. $12, or 121%, (of cost) is gained; cost = $a. 

2. $8, or 162%, is lost; cost = $a. 

3. $24=cost; 334% is gained; selling price = $a. 

4. $35 = cost; 142% is lost; selling price = $2. 

5. $36 = selling price, which includes the cost and a gain of 
20% of the cost. $36 = cost + 4 of cost, or $ cost; $36 is $ of Ha. 

6. $28 =selling price, which is the cost less a loss of 20%. 
What part of the cost is the loss? The selling price is of the 
cost; $28 is - of $y. 


7. Bought a bicycle for $80 and sold it for $100. My gain per 
cent was «. 


8. If I had sold it for $60 I should have lost $y, or w per cent 
of cost. 


9. An importer bought silk at $2.50 a yard and sold it to a 
retailer for $3, who sold it to the wearer for $3.50. What per cent 
of profit did each make ? 


10. Sold a watch for $119 and gained 162%. How much should 
I have gained or lost if I had sold it for $100 ? 


11. A thrifty clerk resolves to live on 60% of his salary. He 
spends $48 more than he intends, but still saves $300. What was 
his salary ? 


12. I paid $125 for what I thought was 4-foot wood. It proved 
to be but 45 inches long. What deduction should be made in the 
settlement ? | 


13. Sold telephone stock for $25,000 at an advance of 25% on 
what I paid for it. What did I gain? 


14. I purchased a patent for $8000. The seller lost 84% of its 
original value. What was its original value ? 


Wratten PERCENTAGE: BUSINESS, PROBLEMS 145 


1. Which is more profitable, buying meat at 16¢ and selling at 
19¢, or selling potatoes at 64¢ that cost me 56¢? 

2. Butter sold at 28¢ yields no profit. What would be gained 
on $140 worth sold at 30¢? 

3. Milk bought at 20¢ a gallon is sold at 8¢ a quart. What per 
cent is gained if 25% of the quantity bought spoils ? 

4. A 5% increase in wages means $200 more a month for the 
employer to pay. What was his annual pay roll before and after 
the increase ? 

5. Mr. H. earns $1200 a year selling carriages at 15% commis- 
sion, all expenses paid. The manufacturer makes a net profit of 
142%. If 50 carriages are sold, what is their average cost ? 

6. A dishonest dealer buys 50 gallons of alcohol at $2.50 a 
gallon, adds 14 gallons of water, and sells the mixture at 10% below 
actual cost. What per cent does he gain ? 

7.. I am offered a 10% discount on a suit of clothes marked to 
sell at $60. I know that even then the dealer will make 121%. I 
offer $50 and get the suit. What per cent does the dealer gain ? 

8. I sell 2 of a lot of land at % the cost and get $200 for the 
remainder. The original cost being $1200, what is my per cent of 
loss ? 

9. What per cent is gained by selling coal at the rate of 4 of a 
ton for what 1000 pounds cost ? 

10. A farmer’s sheep cost him $200. One out of every seven 
dies and he sells those that remain for $275. What was the gain 
per cent, the cost of keeping being $40? 

11. A merchant sold a stock of goods for $3042 and gained 17%. 
What per cent would he have gained or lost had he sold it for 
$2392 ? } 

12. For what should he have sold it to gain 100%? 

13. I bought a $6 umbrella at 162% discount. The dealer made 
25% profit. What did it cost him ? 


146 INTEREST Oral 


1. If I pay 6¢ for a year’s use of a borrowed dollar, what is the 
rate of interest ? 


2. What does the expression “6 per cent interest”? mean ? 
3. At 6%, what is a year’s interest of $300? 


4, What part of a year is 2 months? If the interest for 1 year 
is $18, what should it be for 2 months ? 


5. What is the interest of $400 for 1 year and 6 months at 5%? 
6. At 7%, what is the interest of $200 for 2 years, 6 months ? 


7. What is the first step in finding the interest of any principal ? 
The second step ? 
8. Explain: 21 x 0.07 x $200 = $ a. 

This is called the general method of finding interest. It may 
always be used, but the work may be shortened by some of the 
special methods. 

At 6% the interest of any principal for : — 

12 months = 6% of it. 
2months= 1% of it. (Why?) 
20 months = 10% of it. (Why ?) 
200 months = 100% of it, or the principal itself. 


9. Find the interest at 6% of $380 for 2 yr. 7 mo. (81 mo.). 
PROCESS 
Interest for 20 months = $38.00 Observe that the time was so 
Interest for 10 months = $19.00 separated as to avoid multiplying 


Interest for 1 month 1.90 by anything except 10. 
Interest for 31 months = $58.90 


10. Into what convenient parts would you separate the time if it 
were 26 mo.? 387mo.? 3yr.7mo.? Syr.8mo.? 3yr. 11 mo.? 
lyr.7mo.? 8 yr. 4 mo. ? 


Written INTEREST: RATE 6% 147 


Explain the following process of finding the interest at 6% :— 


TV.) Of $7 Zosforss yriikl mo. 2. Of $278 for 1 yr. 7 mo. 

Interest for 47 mo. of $725. Interest for 19 mo. of $278. 
[ 20 mo. = $72.50 (20mo.= 27.80 
|20mo.= 72.50 Int. for { 1mo.=__ 1.39 

ah eOr 4 wo: 0, eee Sal (19 mo. = $26.41 
| 2mo.= 7.25 


[47 mo. = $170.375 
Find the interest at 6% :— 


3. Of $280 for 2 yr. 8 mo. 7. Of $649 for 7 yr. 8 mo. 
4. Of $640 for 3 yr. 7 mo. 8. Of $750 for 8 yr. 4 mo. 
5. Of $95 for 4 yr. 11 mo. 9. Of $ 295.75 for 5 yr. 11 mo. 
6. Of $73.50 for 1 yr. 4 mo. 10. Of $641.86 for 3 yr. 3 mo. 


TIME IN DAYS: INTEREST 6% 
Oral and Written 


1. How many days in an interest month? In an interest year? 
2. 60 days is what part of a year ? 


3. Since at 6% the interest for a year is 6% of the principal, the 
interest for 60 days 1s #% of the principal. 
4. The interest for 6 days is what part of the interest for 60 days ? 
At 6% the interest of any principal for : — 
60 days =1%, or zr, of tt. 


6 days = 0.1%, or zp Of tt. 
5. Find the interest at 6% of $720 for 75 days. 


PROCESS 
Interest for 60 days = $7.20 6. How was 15 days’ in- 
Interest for 15 days = _ 1.80 terest found from 60 days’ 


Interest for 75 days = $9.00 interest being known ? 


148 INTEREST: BANKERS’ METHOD Written 


Explain the process of finding the interest at 6% :— 


7. Of $196 for 115 days. 8. Of $119 for 89 days. 
Int. for 115 da. of $196. Int. for 89 da. of $119. 
( 60 da. = $1.96 ( 60 da. = $1.19 
30 da.= 0.98 20 da. = 0.3966+ 
int. for-3 20 ‘da, —"— 06538 Int. for 4 6da.= 0.1190 
| 5da.= _ 0.1633+ B8da.= 0.0595 
[115 da. = $ 3.7566 89 da. = $ 1.7651 
What shall I pay at 6% for the useof:— Find the interest at 6% : — 
9. $780 for 67 da. ? 14. $94 for 200 da. 
10. $640 for 98 da. ? 15. $762 for 5 mo. 14 da. 
11. $92 for 3 mo. 12 da. ? 16. $815 for 86 da. 
12. $87.50 for 117 da. 7? 17. $924 for 8 mo. 11 da. 
13. $106 for 2 mo. 17 da. ? 18. $17.84 for 17 da. 


In distinction from the general method, this is sometimes known 
‘as the bankers’ method. 
INTEREST AT ANY RATE: BANKERS’ METHOD 


1. If the interest at 8% = $18, the interest on the same sum 
and for the same time at 1% =a. At5d%=5 x $4a=—_. 


2. If the interest at 6% = $42, the interest at 7% = $a. 


To find the interest of $105 for 75 da. at 5%. 


PRocEsS 3. Show how the in- 
6% int. for 75 da. of $105. terest at 6% is found. 
6% int. for 60 da. = $1.05 4. At1%; at 5%. 
6% int. for 15 da.= 0.2625 5. What if the rate had 


6)$1.3125 =6% int. been7%? 10%? 12%? 
0.2187+=1% int. 
$1.0988 =5% int. 


2 


Written INTEREST 149 


Find the interest of : — 
6. $640 forl yr. 8mo.at1%. (4 of 6%.) 
7. $270 for 3 yr. 10 mo. at14%. (4 of 6%.) 
8. $382 for 1 yr. 9 mo. at 2%. (4 of 6%.) 
9. $927 for 6 mo. 4da. at 3%. (4 of 6%.) 
10. $864 for 2 mo. 7 da. at 4%. (6% — 2%.) 
_ 11. $318 for 1 mo, 13 da. at 5%. (6% —1%.) 
12. $725 for 29 da. at 7%. (6% +1%.) 
13. $649 for 67 da. at 74%. (6% + 11%.) 
14. $84 for 54 da. at 8%. (6% + 2%.) 


THE ONE DOLLAR METHOD 


_1. What two methods of computing interest have previously been 
resented ? 


2. In which one did you first find 6% interest ? 


Note. <Any method in which the interest at 6 % is first found may be called a 
‘6% method.’ 6%, is a very usual rate of interest. It is the legal rate in 80 or 
' more states. It is the rate that is understood when no other is mentioned, 


3. What is the interest of $1 for 1 year at 6%? For 2 mo.? 
For 6 days ? 
At 6% the interest of $1 for: — 
lyear =$0.06 
2 months = $0.01 
6days =9$0.001 


4. Hind the interest of $1 for 2 yr. 8 mo. 18 da. 
Interest for 2 yr. = $0.12 
Interest for 8 mo. = 0.04 
Interest for 18 da. = 0.003 
Interest for 2 yr. 8 mo. 18 da. = $ 0.163 
5. Compared with the interest of $1, what will be the interest 
of $75? Of $183? Of $240? Of $360? 


150 INTEREST: ONE DOLLAR METHOD Written 


1. [hire $ 48.96 at 7% for 3 yr. 7 mo.19 da. What shall I pay 


on settlement ? 


2. Explain the four steps in the process : — 


I. Finding the interest of $1 at 
6%. 

II. Finding the interest of the 
given principal at 6%. 

III. Finding interest at the given 
rate. 
IV. Finding the amount. 

3. What will discharge a debt of 
$475 which has been drawing 5% 
interest for 2 yr. 11 mo. 24 da.? 

4. Find the amount of $7000 at 
4% for 3 yr. 3 mo. 13 da. 

5. I hold two notes of $731 each, 
one at 5% interest, the other at 8%. 
They have been running 4 yr. 8 mo. 
17 da. What shall I receive at settle- 
ment ? 


PROCESS 
Interest of $1 at 6%. 
Ord yrs =e Ui Lo 
For? mor 0.035 
For 19 da. 0.0032 
ie $ 0.2182 
48.96 


— 


816 
39168 
4896 
9792 
II. 6)$10.68144 at 6% 
1.7802 at1% 
PETS) $2.46 at 7% 
48.96 = Prin. 
ve $ 61.42 = Amount. 


Find the amount under the following conditions : — 
6. Principal, $ 84.75; rate of interest, 4%; time, 3 yr. 15 da. 
7. Principal, $942; rate of interest, 5%; time, 4 yr. 1 mo.7 da. 
8. Principal, $193; rate of interest, 7%; time, 18 mo. 27 da. 
9. Principal, $ 64.50; rate of interest, 8% ; time, 5 yr. 5 mo. 5 da. 
10. Principal, $712.10; rate, 9%; time, 7 yr. 4 mo. 29 da. 


11. 4 yr. 6 mo. 21 da. $ 425.50, 3%. 


12. What is the difference between the interest of $810 for 5 yr. 


7 mo. 6 da. at 6%, and the interest of $865 for 5 yr. 7 mo. 6 da. at 


6%? Use a short method. 


13. What is the interest of $5000 for 6 yr. 4 mo. at 4%? 


Written TIME BETWEEN DATES 151 


1. Find the time from June 24, 1903, to Aug. 18, 1907. 


IRST PROCE 1 
First Process Explain the process. 


1907 yr. 8 mo. 138 da. Notre. This method is generally used when 30 da. 
1905 yr. 6 mo. 24 da. is considered a month, When the exact number of 
4 yr. 1 mo. 19 da. days is wanted, the method is shown below. 


SECOND PROCESS 
aa B 
From June 24, 1903 to June 24,’07= 4yr., or 6/03 to 6/0T= 4 yr. 
From June 24, ’07 to July 24,’07 = 1mo., or 6/07 to 7/0O7= 1 mo. 
From July 24, ’07 to Aug. 13, 07 =20 da.,_ or 7/24 to 8/13=20 da. 


2. Find the time (exact) from Sept. 14, 1902 to Mar. 11, 1905. 


Hzplain each process. 


Process A Process B 
PTOMPOept..02 Wnoentywe Uo ==, ory. oF.9/02 to 9/05 ==. 3 yr. 
From Sept. 14 to Feb. 14 = 5 mo., or 9/14 to 2/14= 5 mo. 
From Feb. 14 to Mar. 11 = 26 da., or 2/14 to 3/11 = 26 da. 


3. What advantage has Process B over Process A ? 


4. Why is it well to know the months by their numbers as well 
as names ? 


5. In Process B, what is found at the left of the inclined line ? 


At the right of it? 
6. Napoleon was born Aug. 15, 1769, 


PROCESS 
8/1769 to 8/1820 = 51 yr. and died May 5, 1821. How long had 
ived ? 
2 5 EER aoa Uerntas ene bee | 
4/15 to 5/5 eee 7. Find the time from May 22, 1898, 


to June 12, 1904. 
8. Find the time from Dec. 25, 1901, to Mar. 3, 1905. 
9. How long from 4/18, ’04, to 3/11, ’07 ? 
10. Find your exact age to-day. 
11. Find the time from May 9, ’03, to June 12, ’05. 
12. How long to-day since Aug. 20, 1903 ? 


152 INTEREST: SELECTION OF METHODS 


Three methods of computing interest : — 


J. A general method, page 146. 
IJ. The bankers’ method, page 148. 
III. The one dollar method, page 149. 


Any of these three methods may be used exclusively, byt as no 
one method is always the best, it is well to learn to choose the one 
that will give an accurate result most quickly. 

Solve the following problems by each method, compare results, 
and tell which method you prefer, and why. 


1. Find the interest of $360 at 7% for 207 da. 
2. What is the amount of $75 at 8% for 3 yr. 4 mo.? 
3. What shall be paid for the use of $723.70 for 85 da. a8 10% 


interest ? 
What is the interest under the following conditions ? 


PRINCIPAL TIME RATE PRINCIPAL TIME RATE 


4. $648 lilda. 4%. 9. $432. lyre 8-0.) (eb) ae 


5. $324 167da. 5%. 10. $767.80 3yr.11mo.9da. 51%. 
6. $750 200da. 9%. 11. $ 50.40 10 mo. AL. 
7. P42T)) 93 'da. LG EF 4 eG STs 114.da. 6%. 
8. $865 48da. 4%. 13. $137.77 4yr.9mo. 25 da. 74%. 


14. Interest is the product of: what three factors ? 


15. Which method of finding interest is best when principal, rate, 
or time is divided by 4? By 44? 6? Q9or12? Why? 


16. Which method uses the aliquot parts of the time ? 
17. Which are “6% methods”? Why so called ? 


18. Which is the best method when there are years, months, and 
days in the time, and when cancellation is impossible ? 


19. What is the interest of $400 at 10% for 24 yr? 


EXACT OR ACCURATE INTEREST’ 153 


1. Incomputing interest for parts of a year we commonly consider 
30 days a month and 360 days a year. In taking 51, of a year’s 
interest to find the interest for 1 day, do we take too much or too lLit- 
tle, considering the actual length of a year? 


2. Exact or accurate interest is reckoned for the actual number of 
days in the given time, and counting 365 days to the year. It is 
used by the United States government and sometimes by others in 
business transactions. It differs from common interest only as 
applied to parts of a year.. What part of a year is August?  Feb- 
ruary? The last three months of 1896 ? 


3 zs 1s what part of s4,? Explain this process : — 


di ep at aol 
Gib: 0 3'6.0 3865 


3 
4. If 1 day’s accurate interest is 72 of 1 day’s common interest, 
what is the accurate interest when the common interest is $146? - 


5. If from the common interest I deduct ps of itself I shall 
have the exact interest. Explain. 


Common interest decreased by 73 of itself is exact interest. 
6. Find the accurate interest of $500 for 90 days at 4%. 


7. Find the exact interest of $1000 at 3% from May 9 to 
Sept. 4. 


Notre. The exact number of days must be found; that is, 22 + 304 31 + 
eee =.118. 


Find the exact or accurate interest of — 
8. $800; 6%; Aug. 11 to Oct. 9. 
9. $720; 8%; Jan. 4 to Mar. 15. 

10. $1200; 3 mo. 12d.; 5%. 

11. $1500; 72 d.; 10%. 


12. What is the exact interest of $1000 for 2 yr. 249 d. at6%? 
(Find common interest for 2 yr. + exact interest for 249 d.) 


154 INTEREST Written 


Nore. The method to be employed in the solution of the following problems 
is shown by the Roman numerals I, II, III (page 152). 


1. What is the interest of $840 for 9 mo. 17 da. at 4%? I. 
2. Find the amount of $722 for 156 da. at 12%. II. 


3. What will settle an account of $425 that has been drawing 
interest of 5% for 5yr.5mo.? III. 


4. May 17, 1903, I borrowed $ 248 at 22%. 
much interest had accrued? III. 


Aug. 15, 1905, how 


5. In41 yr. how much will be received on a $5000 railroad bond 
paying 2% semi-annually ? I. 


6. May 27,1904, I paid a note of $475.28 that had been drawing 
4% interest since Dec. 31, 1900. III. 


Find by inspection the best method of solving the following problems, 
and use it in finding the interest. Try to forecast the result : — 


7. $90,000 on interest 7 mo. 24 da. at 4%. 
8. $728 draws 5% interest for 20 months. 
9. 54% interest of $900 from Jan. 15 to Nov. 2. 
10. Principal, $72.59; time, 125 days; rate, 121%. 
11. What shall I pay for the use of $500 for 50 days at 5%? 
12. $320; 74%; July 7, 1898, to Aug. 4, 1902. 
13. $720; 8%; Oct. 19, 1900, to May 11, 1903. 


14. $472 3% 112 da. 20. 3% $872 4 yr. 8 da. 
15. $648 41% 8 mo. 21. 5% $5000 16 mo. 
16. $800 23% 180 da. 22. 24% $178.91 104 da. 
17. $2000 7% 194 mo. 23. 1% $3294 178 mo. 
18. $4000 4% 42 yr. 24. 41% $700 412 yr. 
19. $950 9% 248 da. 25. 8% $64.87 295 da. 


Oral COMMERCIAL DISCOUNT LO 


1. Show the difference between grower or producer, importer, 
wholesaler, retailer. 


2. Do you buy from wholesalers or retailers ? 


3. With whom do wholesalers have to deal ? 


It is the general custom of wholesale dealers, manufacturers, and 
publishers to fix a price on their goods and then allow a certain per 
cent discount from this price to “ the trade”; that is, to retail dealers 
handling their kind of goods. 


4. Pear trees are listed at $1.50 each. As I am dealing in trees 
I buy from the nursery at. $12 per dozen. What discount or reduc- 
tion do I get on each tree? What per cent is this of the list price ? 


5. A man is trusted for goods billed at $100. He is to pay in 
3 months. How long is the term of credit ? 


6. The dealer offers to sell the same goods for $98 cash. Why 
is this? How much does he discount for cash? What per cent of 
the list price is this ? 


7. The price of knives per dozen is $2. By buying 30 dozen I 
get them for $50. What discount did I get by buying in the larger 
quantity ? What per cent was this ? 


8. If I had bought 100 dozen the net price, or what I actually 
paid, would have been $1.60 per dozen. Is this a larger or smaller 
rate of discount than offered on 30 doz.? Why is this ? 


9. The discount on a car load of coal is 10%, or $8. What is 
the gross price of the car of coal ? 


10. The list price of a bill of goods is $40. The net price was 
$32. What was the discount? What per cent was this of the list 
price ? 

11. The list price of hats was $36 a dozen. The retailer sold 
them at $4 each and doubled his money. What rate of discount 

‘did he receive on the list price ? 


158 DISCOUNT Oral and Written 


1. A $4000 house is offered at $3500 cash. What discount was 
offered for cash? What per cent is this ? 


2. Bought $200 worth of flour. If I need not pay for 6 months, 
what do I save by not paying until the end of 6 months ? 


3. Which customer should receive the larger discount, one who 
pays cash, one who pays in 3 months, or one who pays in a year ? 


4. I buy $400 worth of goods. The dealer does not require me 
to pay for 6 months, but gives me a time discount of 2% if I pay 
within 3 months from the date of purchase, or 4% cash discount if I 
pay cash. What will the goods cost me if I pay cash? If I pay 
within 38 months? If I pay at the end of 6 months ? 


5. On the bill heads of wholesale houses there is usually a note 
showing what discounts are allowed. Thus, “Terms: 60 days, 2% 
10 days.” Explain what is meant. 


6. Explain: “Terms: 90 da.,4% 30 da., 6% 10 da.” 


7. I bought $400 worth of goods May 1. “Terms: 3 mo. or 4% 
off 60 da. or 10% off 30 da.” What will settle the bill May 28 ? 


Discount is always a part, or per cent, of the price which tt reduces. 


Written 
Find the missing terms : — 

AT, OF BILL % eget Net Cosr Hane SORES List Price | % 
1 $ 2000 5 x 8 $ 24 $ 600 x 
2 $ 900 x $ 810 9 x . $ 150 1 
3 % 2 $ 490 10 $ 20 — x 4 
4 $ 1200 6 x 11 $ 36 $ 1800 x 
5 $ 1850 x $ 1786 12 a $ 1400 5 
6 x 5 $ 1900 13 x $ 2200 2 
if $ 2400 a $2000. | 14 $18 $ 900 x 


Oral and Written SUCCESSIVE DISCOUNTS 159 


It frequently happens that wholesale merchants send out expen- 
sive catalogues containing a description of their goods, in which is 
quoted a certain list price. The retail dealer gets a discount from 
this list price. When a further discount can be given, it is the 
custom: to quote another discount that is to be taken from the former 
discounted price, rather than a new discount on the list: price. 


1. I buy a bill of goods listed at $400. The discounts are 25% 
and 10%. What is the net price ? 

Explain: $400 — 25% of $400 = $300; $300—10% of $300 
= $ 270. 


2. I buy an organ listed at $150. Being a music teacher, I get 
a discount of 20%, and a further discount of 5% for cash. What 
does the organ cost me ? 


3. I am offered my choice of 10% discount, or two successive dis- 
counts of 5% each on a bicycle listed at $100. How much shall I 
gain by taking the better offer ? 


4. I can buy $480 worth of pressed bricks of Henry Clay & Co. 
at the discounts of 15% and 5%. Another firm offers me two 10% 
discounts. Shall I accept the first or the second offer? Why ? 


5. I receive the following estimates for a miscellaneous lot of 
hardware : — 
$ 476 with three 5% discounts. 
$ 508 with two 10% discounts. 
$ 492 with a 15% and a 5% discount. 


Which is the better offer ? 


Find net prices : — 


List % OFF Teer % OFF 
6. $15.40 20 then 5. 9. $14.85 60, 10, and 2. 
7. $49.50 50 then 2. 10. $320.15 20, 5,and 1. 


8. $600 45 then 3. 11. $4000 30, 12, and 3. 


160 DISCOUNT Written 


1. One buyer gets 30% off, another gets 25% and 5%. Give net 
cost to each on a shipment of $ 2000 gross value. 

2. A furniture maker allows 15% from the list price. _ Find the 
net cost on an order amounting to $ 12,488, including $118 for cart- 
ing, which is without discount. 


3. Tubing listed at $10,000 is billed less 60% and 2% for cash. 
Net cost = $ x. 

4. The trade discount on certain goods is 70%. Large buyers 
receive a second discount of 10%, making the total discount 7%. 

5. List price, $500; net, $425; discount, $a; rate, y%. 

6. List price, $ 488.90; net, $391.12; discount, $a; rate, 7%. 

7. 1800 ft. of moulding at 20%, less 12% to the trade and 1% for 
cash, cost $a. 


8. A shipment of sugar invoiced at $11,000 is subject to a rebate 
or reduction of 5%. Terms: 15 days. 149% off. for cash makes the 
net cost $ x. 


9. The discounts on a $1000 invoice are, not 45%, but 30%, 
10%, and 5%. Find the net cost. 


10. On an invoice of flour amounting to $ 648, I receive three suc- 
cessive discounts of 5%. What was the net cost of the flour? 


11. A dealer in agricultural implements sends me his price list, 
and offers discounts of 40, 15, 7, and 5%. I order a bill amounting 
to $1500 according to the price list. What shall I actually pay ? 


12. I order of the White Publishing Co. :— 


13 books listed at $1.50 
10 books listed at 1.75 
15 books listed at 1.10 
1 set Dickens at $ 18, and 12 vols. at 90¢. 


I receive a dealer’s discount of 162% and 2% for cash. Find the 
net cost. 


Oral INSURANCE 161 
1. If the owners of a hundred ships agree to share the loss if 
one is wrecked, who might profit by the arrangement ? 


2. Mr. Smith owns a $3000 house. By spending $30 he can 
be sure that 2 of his loss by fire will be made good. Many others 
do the same and from their money losses are paid. If Mr. Smith’s 


house is burned, what will he receive ? . 


3. An Insurance Company agrees to pay part of the loss of ~ 
those having paid a certain per cent or premium on the insurance of 
their property. What will it cost a man to insure for $ 250 at 14% ? 


4. 100,000 persons pay 25¢ each to an accident insurance com- 
pany. If it pays $15,000 in claims for injuries, and $4000 for 
expenses, the profit is $a. Who is the insurer ? Who are insured ? 


5. The agreement to make good a loss on certain conditions is 
printed in a policy made by the underwriter or insurer, and held by 
the insured. The cost of a $ 25,000 policy at 3% a year is $a. 


6. By paying an annual premium a person may be assured that 
at his death or at a certain age, his family, or he himself, will receive 
a certain sum. How will this money have been obtained ? 


7. A ship, costing $210,000 is insured for 2 of its value at 2%. 
If lost, the owner receives $a. The underwriters lose $y. 


8. $40 pays for five years’ insurance on a brick store which cost 
$5000. The insurance valuation is $4000. What is the annual 
rate ? 

9. A wooden tenement house two miles from a fire-engine is 
insured for 3%, but only for one year. If the valuation is $4000, 
the cost for five years is $a. The property insured is called a risk. 
Compare the last two risks. : 


10. Insurance provides for sharing loss due to what causes ? 
11. A schoolhouse is insured for five years at 4% premium, 


which is $300. The insurance valuation is 2 of the cost of thé 
house. What is the underwriter’s loss if it burns ? 


162 INSURANCE Written 


1. A stock of goods is worth $12,000. The premium for a year 
is 1%, or $100. What is the insurance valuation? If destroyed 
what will the underwriters pay ? What.will the owner lose besides 
the premium ? 

2. Why is property usually insured for less than its full value ? 
A $7500 house is insured at 14% for $62.50. What was the insur- 
ance valuation? 


Supply values for x :— 


InsuRANCE RaTE% PREMIUM INSURANCE Rate % PREMIUM 
3. $15,000 My $ 200 6. a + $ 10 
4. $ 7000 x $ 84 7. $7500 14 x 
5. a 4 $ 60 8. $4740 2 a 


9. A factory worth $60,000 is insured for # its value at 12%. 
The possible loss to the owner, including the premium, is $2. 


10. $175 was the premium on ? the value of a collection of paint- 
ings, at 1% a year. What was the value of the paintings ? 


11. $1960 is 98% of the insurance. $40 was the premium. 
What was the rate of premium ? 


12. A house was insured for # of its value at 14% premium, the 
premium being $27. Required the value of the house. 


13. The cargo of the Neptune is insured for 2 of its value, at 2%. 
What is the value of the cargo? ‘The premium paid is $3750. 


14. At the age of 32 a gentleman insures his life for $8000. The 
annual premium is $120. If he dies at the age of 44, what per cent 
of the insurance will he have paid as a premium ? 


15. A manufacturing company pays an average premium of 74% 
on its plant. In the annual report of expenses, $280 is entered as 
cost of insurance. What is the value of the plant if insured for 80% 
of its value ? 

16. A manufacturer pays $800 premium, at 2%. ‘The property 
‘is partly destroyed by fire, and the adjuster settles with him for 
25 % of the insurance. What does he receive ? 


Oral or Written ; COMMISSION 1638 


Selling through an Agent 


Farmers, fruit growers, and other producers, as well as the mer- 
chants of the cities and towns away from commercial centers, 
usually ship their produce to agents or commission merchants in some 
city, rather than take it there themselves and then seek a buyer. 

When an agent sells goods for another without actually receiving 
the goods, he is usually called a Broker. 

The commission merchant usually charges a per cent of the amount 
sold as his fee or commission. 

The one who sends the merchandise to be sold is the principal, 
shipper, or consignor. 


1. I send a shipment of berries to a commission merchant in 
Chicago. He sells them for $100. His rate of commission is 14%. 
What does he keep, and what does he send to me ? 


2. A commission merchant received 3000 melons which he sold 
for 50¢ each. What was his commission at 2% ? 


3. My agent, a commission merchant in New York, charges me 
5% for selling a consignment of fruit. What were the sales if his 
commission was $20 ? 


4. IL receive $14 for selling $700 worth of flour. What was my 
rate of commission ? 


5. I sold through a commission merchant 100 bu. of potatoes at 
50¢ per bushel, allowing my agent 2%. What were my net receipts 
from the sale ? 


6. I shipped 100 baskets of peaches to my agent. He sold them 
at $1 per basket. His commission was 5% and the freight twice as 
much. What did I receive from the sale ? 


7. A commission merchant charged me 15¢ a crate for selling 
strawberries. What per cent was this if they sold for $3.00 per 
crate ? | ; 


8. My commission at 5% was $18. What were the sales ? 


164 COMMISSION Written 


Selling through an Agent 


1. How much does a broker receive for selling 1500 barrels of 
pork at 3%? The pork sells at $7.83 per barrel. 

2. A dealer buys 1000 doz. of eggs at 13 ¢, and sells them through 
a commission merchant at 19¢. What were his profits if the com- 
mission was 2%? Expressage $3.40. 

3. A western merchant received a commission of 20% for selling 
harvesting and mowing machines. During one season he sold 6 
harvesting machines at $115 each, and 4 mowing machines at $85 
each. ‘The cost of selling and delivery was $37.50. What was his 
net gain ? 

4. Sold goods at auction, amounting to $11,450. The charges 
were: commission, 24%; storage, 14%; and advertising, $21. What 
were the net receipts ? 


What is the rate of commission when an agent receives : — 


5. $100 on $15,000 ? 9. $4.50 on $300 ? 
6. $29.43 on $981 ? 10. $128 on $896 ? 
7. $1517.92 on $85,896 ? 11. $21.50 on $615 ? 
8. $112.50 on $4500 ? 12. $2.58 on $86 ? 


13. An agent received $54.50, including $4.50 for surveying, 
deed, etc., for selling a house valued at $2500. What was the rate 
of his commission ? 

14. A purchased 350 bu. of corn at $1 per bushel, and B sold it 
at a commission of 3%. If the selling price was $1.15 per bushel, 
what were B’s commission and A’s profit ? 

15. The selling price was $6000, the commission was $240, and 
the other costs of the sale were $18; the net gain was $742. What 
was the rate of commission? The cost ? . 

16. During the coal strike of 1902, a man sold 760 tons of coal as 
follows: 10% of the whole amount at $12 per ton, 25% of it at $11 
per ton, and the remainder at $10 per ton. Brokerage on the whole 
amount 2%. What were his net receipts ? 


Oral COMMISSION 165 


Buying through an Agent 


1. If I employ an agent, or correspondent, to buy goods for me, 
I must pay him a per cent of whatever amount he expends for my 
benefit. If he buys $1000 worth of corn for me at 8% commission, 
what must be my remittance to him for the corn and his commission ? 


2. An agent buys a horse for me at $200. His commission is 
2%. How much, money shall I send him ? 


3. My agent buys 250 bbls. of cement for me at $2 per barrel. 
What is the amount of my remittance to him if his commission is1% ? 


4. I telegraph my agent to buy 10,000 bushels of wheat at 90. 
Tallow him 2%. How large a check should I send him to cover the 
whole transaction ? 

5. An agent netted $80 per month after paying $5 for office 
expenses. What were his sales if his rate of commission was 2% ? 


6. A collector sends his principal $180. He collected $200. 
What rate did he charge? 


7. A boy earns $6 per week collecting gas bills at 4%. What 
are the net proceeds to the gas company ? 


8. An agent buys $2000 worth of copper, charging 1% commis- 
sion. What shall the principal remit to the agent to pay for the 
copper and his commission ? | 


9. I remitted $102.50 for buying umbrellas at 24%. What had 
the agent spent for umbrellas ? 


10. An agent charges 14% for buying chair stock. How large a 
check shall I send him if I wish him to buy $1000 worth of stock 
for me? 


11. A broker buys pork at 1% commission. How much did he 
buy if his commission was $17.50? 


12. I remit my agent $2040 for buying $2000 worth of hay for 
me. What was his rate of commission ? 


166 COMMISSION Written 


1. A remittance of $669.50 is the purchase price of wool, and a 
commission of 3%. What is the commission ? 


2. I have remitted to an agent $1332.50 for flour at $6.50 
per barrel. His commission was 24%. How many barrels did 
he buy ? 


3. A broker received a sum of money to expend, after deducting 
his brokerage of 1}%. He spent $2400. What was his brokerage ? 


4. An agent received 5% for selling wool. His commission 
amounted to $208.50. How much did he pay for the wool ? 


5. Senta broker in Minneapolis a draft for $603.75 for the pur- 
chase of flour. Brokerage 5%, and the flour $5 a barrel. How 
many barrels were bought ? 


6. I received a remittance of $2639 for a bill of coal and my 
commission of 14% for buying. Required my commission. 


7. What are the net proceeds from a sale of 1000 tons of hay at 
$11.75 per ton? Commission 14%. 


8. My agent sells cotton at a commission of 54%. He remits to 
me $2929.50. What was his commission ? 


9. My agent sells 500 bbls. of flour at $10 a barrel, and sends me 
a check for $4750. What rate of commission did he charge ? 


10. Received a consignment of 3000 bu. of corn, with instructions 
not to sell for less than 56¢, and that all received over 60¢ was to 
cover the commission. I sold at 65%. The rate of commission 
was & %. 


11. The remittance for the purchase of lumber was $3668.25. 
The rate of commission was 4%. How many thousand feet of lum- 
ber were bought at $36.50 per M. ? 


12. A promoter received $50,000 for effecting a combination of 
furniture manufacturers whose united capital was $1,800,000. What 
was the rate of commission paid for the promoter’s services ? 


Written REVIEW PROBLEMS 167 


Discount, Commission, and Insurance 


1. On a bill for hardware amounting to $480 I received four 
successive discounts of 10% each. What was the amount paid ? 


2. My residence is insured for 2 of its value in the Provident 
Insurance Co. at }%. The premium is $40. What is the value of 
my property ? 


3. My agent in Mobile bought 40,000 Ib. of cotton at 97%. His 
commission is #% and his expenses are $143.75. What shall I 
remit him ? 


4. A real estate broker sells a farm for $8000 at a 5% commis- 
sion. What are the net proceeds of the sale, and what is his com- 
mission ? . 


5. I can buy 1000 bbl. of oil at $1.124 with 3% off in 30 days, 
or 5% off for cash. What shall I save by accepting the better offer, 
money being worth 6% ? 


6. The estimated loss of property at a large fire was $275,000. 
The insurance received was $180,000. How much must be taken in 
new risks at an average of 2% to cover this loss to the underwriters 
together with $5000 expenses ? 


7. I receive from my agent in London a draft for $3860, the net 
proceeds of a sale of flour at 81% commission. What were the gross 
proceeds ? 


8. A drummer earns $2500 annually. $1000 is a guaranteed 
salary; the remainder is his commission of 5%. What are his 
annual sales ? 


9. A broker negotiates a loan of $6500 on a real estate mortgage. 
His commission is 2%, and the expenses of examining title, etc., are 
$72.37. What does the mortgager receive ? 


10. Bought 1000 gross of screws at 27 cents, with a discount of 
15,10, and 5. I sold the lot at cost plus 30%. What was my gain ? 


168 COMMISSION: REVIEW Written 


Supply values for « and y (dealing with selling agents) : — 


even EXPENSES PRA oF COMMISSION NET PROCEEDS 

1. $437 0 2% w | y 

Bane act $ 47.50 1% $ 27.50 y 

3. $250 a y $ 25 $ 200 

4. 2 0 2% y $ 900 

5. $1200 $ 100 x $18 y 

6. $1680 x 4, y $ 60 

1 @ 0 y $ 13.52 $ 437.18 


8. $430 is received from a sale of linen. After retaining 14% 
commission and paying $2.50 for advertising the sale, what is the 
balance to be remitted ? 

9. What value of goods can be bought on 5% commission from 
a remittance of $577.50, allowing $24.50 for advance charges of 
forwarding the purchase ? 

10. A correspondent retains 44% on the receipts of a certain sale, 
and after paying $4.87 for carting, etc., remits $200. The gross 
receipts include $%+$y+$z. 

11. A dealer sends to his agent $20,500. This includes a com- 
mission of 2% on what the agent will spend, and $100 for insurance 
and sundries. He spends the balance, $, for wool. 


Supply values for « and y (dealing with purchasing agents) : — 


eiuke i Gs Am’T OF PURCHASE RATE OF oMaatae 
+ FREIGHT, ETC. COMMISSION 
12. $595.80 a y $ 6.60 
13. $179.76 $ 148.30 + $ 27.94 £ y 
14. A) $ 755 y $ 22.65 
15. ax y 5% $ 9.90 
16. $1293.75 2 31% y 


17. 2 $ 684.10 + $88 24% y 


Oral PROMISSORY NOTES 169 


1. Aug. 15, 1903, Edward Hale lends to George Sharp $ 500 to 
be repaid when the lender asks it, together with interest at 5%; as 
evidence of the loan and security for its payment, the lender receives 
from the borrower a promissory note like the following : — 


BIOO__- Chicago, Iil., Auguat Lop elo Oo 


Qn demand, after ee SF promise to pay to the 


with interest at five per cent. 


Value received. 


George Sharp. 


Who is the maker, or the one who promises to pay ? 

Who is the payee, or the one to whom the promise is made ? 
What is the face of the note, or the sum named in it? 
When is the note payable ? 

Why is such a note called a demand note ? 


Why is it called an interest-bearing note ? 


ont ont FF WOW 


A promissory note is a kind of property, and may be bought 
and polG like other property, and hence is called negotiable paper. 


9. Whenever the payee of a note transfers it to the ownership 
of another person he first indorses it; that is, he places his signature 
on the back of it. Who would be the indorser of this note should it 
be sold ? 


10. Write a note to fulfill the following conditions: -maker, E. L. 
Price; payee, A. T. Holmes; face, $300; rate of interest, 6% ; 
demand note dated Chicago, Sept. 26, 1904. Indorse it. 


170 PROMISSORY NOTES Oral 


11. The payee of a note may indorse 
it in blank as in A, or he may make a 
special indorsement, as in B. 


A 


Gdwarid State. 


12. A blank indorsement makes a note 
payable to the holder. <A special in- 
dorsement makes it payable to the per- 
son named by the indorser as payee. 
Copy and indorse the note on page 169. 


B 
ena: / 13. Every indorser of a note is re- 
ay to the order of sponsible for its payment unless the 
IP ENY tall. words “without recourse” precede his 


glgenature, as in C. 
Gdwarid /fate. m : 


14. If the holder of the note on the 
preceding page demands payment on 
Noy. 15, 1903, what amount does Mr. 
Sharp owe him ? 


Cc 15. What will Mr. Hale receive if he 
demands payment on Feb. 15, 1904 ? 


A as eerie 16. Write a demand note from the 

Coa Le following data: face, $300; date, 
Sept. 20, 1904; maker, H. E. King; 
payee, A. L. Hayes; place where you 
live; rate, 6%. 


17. Indorse the note you have written. 


18. Suppose the note sold to H. E. Smith; write a special in- 
dorsement. 


19. Suppose Mr. Hayes is not to be held responsible for the pay- 
ment in case that Mr. King cannot pay Mr. Smith; write the 
indorsement.. 


20. What is due on the note March 20,1905? To whom is it 
due? Who pays it? 


Oral and Written PROMISSORY NOTES rin 


21. If the words “one year,” “four months,” “sixty days,” etc., 
were substituted for the words “on demand,’ when would the 
note (p. 169) be payable? The note is then a time note. 


Note. In some states three extra days after the expiration of the time 
named in the note are allowed the maker for its payment. They are called 
days of grace. Interest is exacted, however, for the days of grace. 


22. If the note (p. 169) were a four months’ note, at what date 
would it be payable without grace? With grace? When, if it were 
a 2 months’ note ? <A six months’ ? 


23. Notes mature, or are legally payable, on the day when the 
time named in them expires, or on the third day thereafter, when 
grace 1S allowed. 


24. All notes that contain the words “with interest” draw interest 
from date unless otherwise specified. All other notes draw interest 
from maturity. When no rate of interest is specified, the legal rate 

is understood. 


Nore. It is quite usual to name in a note the place at which it is payable. 
The place named is generally some bank (see p. 185). 


WRITTEN EXERCISES 


Make interest-bearing notes answering to the following conditions, 
and compute the amount due at settlement. In finding the day of 
maturity, allow three days of grace if that is the custom in your State. 


DATE FACE TIME TO RUN PAYEE RatE SETTLED 
3/17, 04 | $240 | On demand A.B. Rice 6% 9/14, °05 
8/12, ’08 | $800 | One year E. F. Foss 09 WELZ / 18.805 


4/21,’03 | $725 | Four months | Wm. Ward 5% Maturity 
6/15, 04 | $1800 | Six months Thos. True 4% 9/21, ’06 
1/19, °04 $610 | Two years A. M. Bates Bi 127 2a OF 
2/24,°05 | $280 | On demand R. E. Nye 4494 7/16, °06 
1/04 $75 | Sixty days E. B. Hale 12;% Maturity 


gap oy aes sta 


172 PARTIAL PAYMENTS OF NOTES Oral 


1. A note of $300 draws 10% interest. What amount would 
discharge the note at the end of the first year? Suppose that 
instead of the note being paid in full at the time, a partial payment 
of $100 were made, what would then be due? 


2. Would the $100 pay all the interest due? How much of the 
face or principal would it also pay ? 


3. How much of the original $300 does the maker of the note 
continue to keep? On what sum, therefore, should he pay interest ? 


4. Ifthe remaining $ 250 should be used another year, the interest 
on it at 10% would be $a, and the amount due would be $ 230 + $a, 
or $y. 

5. If another partial payment of $100 should then be made, a 
remainder of $y — $100, or $z, would still be left at interest, and 
yet to be paid by the maker of the note. 


6. Give the values of a, y, and z in the solution of the following 
problem : — 

On my note, payable to you for $300, I make a partial payment 
of $100 at the end of each year for three years. What is then due 
you, 10% interest being charged ? 


SoLutTIon 

J. Of your money I have foruse . ? ; $300 

For a year’s use of itat 10% lowe . : x 

At the end of the year I owe you : ‘ $330 

I make a partial payment to you of. : 100 

* JI. This leaves a balance for me to use of ‘ $230 

For a year’s use of this sum I owe you , 23 

At the end of the second year I owe you . . $y 

I make a second partial payment of . : 100 

II. I now have of your money only . ‘ ; $2 
For a year’s use of this sum I owe you : 15.30 
I owe you at the end of the third year ‘ $ 168.30 

If I pay youathird . é : : : 100 


IX a shall stillowe you. P ‘ = $68.30 


‘ 


Oral PARTIAL PAYMENTS OF PROMISSORY NOTES Lis 


When partial payments of a note are made, the holder records the 
amount and date of each payment on the back of the note. 


tia o es Sioux City, Auguet /4, 1904. 


Qn demand, after date, % promise to pay to the 
order of. 
Seven /fundred Twenty 
with interest at ax per cent. 


Value received. 


G: YUN Si bevena ’ 


INDORSEMENTS ON Note 1. Who puts these indorse- 
ments on the note ? 

Reeeived on the within note : 2. Will any other receipt 

Deo. 26, 1905, $200 be requested for the $200 

‘ ; paid Dec. 26, 1905, and if so, 
Sef. /4, 1/908, 175 by whom ? 

Lee, 3/, 1909, 400 3. What needs to be done 

Settled, Lee. 8/, 19/0. before the note can be trans- 


ferred to a third person ? 


Non gee The Supreme Court of the 


United States has decreed 
pnebe —— 


Partial payments of notes must first be used to cancel the interest due. 
Any balance remaining may be used to lessen the principal. 


This decree gives what is called “The United States Rule.” 
Sometimes other rules are used. If your state uses a different rule, 
find what it is and use it. The special rules will not be discussed 
in this book. 


174 


A SOLUTION 


PARTIAL PAYMENTS 


Find the amount due at settlement, Dec. 31, 1910, on the note on 


the preceding page. 
From date of note to 1st payment 
8/14, °04, to 8/14, ’05=1 yr. 
8/14, ’05, to 12/14, 05 = 4 mo, 
12/14, 05, to 12/26, °05 = 12 da, 
Int. of $1 
Interest due when lst payment is made 
Face of note, or 1st principal 
Amount due at time of Ist payment 


lst payment, which cancels interest due, and more 
Remainder which continues to draw Int. ; 2d Prin. 


From 1st payment to 2d payment 
12 /26,')05,. to. 12/26, 0i-e2 2-71, 
12/26, ’07, to 8/26, °08 = 8 mo. 
8/26, 08, to 9/14, ’°08 = 19 da. 


Interest due at time of 2d payment 
2d principal . 
Amount due at time of 2d patent : 
2d payment cancels interest and part of principal 
Remainder which still draws Interest ; 3d Prin. 
From 2d payment to 3d payment 
9 /14,.°08, to °9/14,709 = Ayr. 
9/14, 709, to 12/14, 09 = 3 mo. 
12/14, ’09, to 12/31, °09 = 17 da. 


Interest due at time of 3d payment 

3d principal . ; 

Amount due at time of 3d parment 

3d payment cancels interest and part of principal 


Remainder which still draws Interest ; 4th Prin. 


From 3d payment to settlement 

1270127000 00 12/51, 710 a ye, 
4th principal ‘ 
Amount due at Settlement 


$0.06 $720 
0.02 0,082 
0.002 | 144 
$0,082 57 6 
| $ 59.04 
720. 
$779.04 
200. 
$579.04 
-——_—0.1634 
$0.12 9650 
0.04 173742 
0.0034 34 7424 
$ 0.1632 57 904 
$ 94.48002 
579.04 
$ 673,52 
1G) 
$ 498.52 
0.0773 
$0.06 6) 249260 
0.015 41543 
0.0023 3 48964 
$0.0773—_- 84.8964 
$38.80147 
498,52 
$ 537.82 
400. 
$ 187.32 
0.06 
$0.06 Int. $8,.2392 
137.82 
$ 145.56 


1. How much interest was cancelled by the first payment? How 


much of the principal ? 


PARTIAL PAYMENTS 175 


Payments too Small to cancel Interest Due 
A SOLUTION 
Commonly the partial payment of a note will not only cancel all 
interest, but will also pay a portion of the principal, and thus reduce 
the amount upon which the borrower has to pay interest. It some- 
times happens, however, that the payment is too small to cancel even 
the interest due. In such cases — 


The interest must not be used to increase the principal, which must 
never represent more than the money actually and previously due to the 
holder or payee, and in use by the maker. 


1. What is due at settlement on a note of $600 dated Aug. 15, 
1902, drawing 6%, and indorsed as follows : — 


Dec. 15, 1903, $25? Sept. 15, 1905, $ 200? Settled Aug. 15, 1907? 


SOLUTION 


From date to 1st payment 


S/O 0210 18/108 = evry 9) : . $0.06 
8/15, ’08 to 12/15, 08 = 4 mo. ; : , 0.02 $ 600 
$ 0.08 0.08 
The payment of $25 will not pay the interest due, $ 48.00 


Hence we compute the interest : — 
From date to 2d payment 


3/15,702 to:8'/ 15; "0d = 3 yr.” : ‘ ea Ao 
8/15, ’05 to 9/15, °05 = 1 mo. : ; ; 0.005 $ 0.185 
| Interest of $1. : ‘ ‘ epiacuals| lh. 606 
Interest due at 2d payment F ; : : : $111.0 
Face of note on interest . : } : ; 7 600 
Amount due at 2d payment : : : $711 
Sum of Ist and 2d payments ($25 + ¢ 200) : : 225 
New Principal on Interest , F : : $ 486 
From 2d payment to Wt oient 0.115 
9/15, 705 to 9/16, 06-1 yr. ; : : . $0.06 $ 2.430 
9/15, ’06 to 8/15, 07 = 11 mo. ; f : 0.055 4.86 
$0.115 48.6 
Interest due at settlement . ; : 4 , ( $ 55.890 
Principal due at settlement ; : ; : ! . 486. 


Amount due at Settlement. : : ; $ 541.89 


176 PARTIAL PAYMENTS Oral and Written 


1. Study the solution on the preceding page. Why do we not 
add the first interest, $48, to the principal, subtract the payment, 
$25, and compute the interest on the remainder, $623, as in the 
example on page 174 ? 


2. Is it fair that the maker of the note should pay interest on 
more than he has hired and used ? 


3. Will the two payments together cancel the interest due when 
the last one, $200, is paid ? How much of the principal besides ? 


4. How must we proceed when the payment will not cancel the 
interest due ? 


5. Which is better for the one that owes the money, to subtract 
the amount paid from the amount due when payment is made, 
regardless of the amount of the payment, or do as in the last 
solution ? 


6. Show why the debtor might object to the arrangement pro- 
posed below ? 


I loan Mr. James ; ‘ : 7 $600 
A year’s interest at 5% is . ‘ ; 30 
He then owes me : ! A : $ 630 
He pays me 20 
I ask him to pay me interest on . : $610 


7. What will settle a 5% note for $1000 Aug. 1, 1907, on which 
$50 was paid 2 years after date, and $500 4 years after date? The 
date was Aug. 1, 1899. 


8. What was due May 1, 1905, on a note for $3000, on which 
$100 was paid at the end of each year for 3 years? The rate was 
4%, and the note was given May 1, 1901. 


9. Cyrus Drew gave Frank Watson his note for $800 at 3% 
interest, Aug. 17, 1900. Dec. 23, 1902, he paid $300, and May 29, 
1904, he paid $40. What was due 6 years from date ? 


Written PARTIAL PAYMENTS Lit 


1. A note for $500, dated Aug. 10, 1903, drawing 6 per cent inter- 
est, is paid Aug. 10, 1905. A payment of $100 was made Aug. 10, 
1904. How much was due at time of settlement ? 


2. A note dated May 16, 1904, for $1200, 4 per cent interest, has 
two partial payments of $300 each indorsed upon it, 6 months and 


18 months after date respectively. What will cancel the note 3 
years from date ? 


3. The face of a note is $1500. It draws 5% interest. 8 months 
after date $500 is paid. 20 months after date $600 more is paid. 
At the end of 4 years, what will pay what is due ? 


4. A note of $2000 drawing 6 per cent interest, is dated Jan. 1, 
1904, and is paid Jan. 1, 1907. What is due, provided $500 was 
paid on New Year’s day in 1905 and in 1906 ? 


5. Aug. 20, 1904, Gordon Cook gave Thomas Swan his note for 
$5000 with interest at 8 per cent. Feb. 20, 1905, he paid $2000. 
Aug. 20, 1906, he paid all but $600 of what was due. What sum 
cancelled the note Dec. 26, 1907? Study the problem and use a 
short method. 


6. One half of a note of $7500, with interest at 4%, was paid 
March 17, 1904. What was due 4 yr. 6 mo. from date of the note, 
which was Dec. 12, 1903 ? 


7. I paid a note that had been running just 5 years. It drew 8 
per cent interest, and its face was $900. It was given Dec. 11, 1905, 
and $3800 had been paid on it 2 yr. 8 mo. after date. What can- 
celled it ? 


8. Face, $600. Rate, 6 per cent. Date, May 12, 1903. First 
payment, $50, May 12, 1905. Second payment, $600, June 19, 
1907. What was due Aug. 12, 1909 ? 


9. What is due Aug. 15, 1905, on a note for $1600 drawing 5% 
interest, given May 15, 1903, a payment of $25 having been made 
Dec. 15, 1904 ? 


178 TAXES Oral 


The expenses of towns, cities, counties, and states are met by . 
levying taxes annually on all owners of property. In addition to 
this in most states all male citizens over 21 years of age are re- 
quired to pay a poll tax (poll = head). 

1. Why are some persons taxed more than others ? 

2. Mention several ways in which the taxes collected in your 
city are expended. 

3. What need have county and state to raise money by taxation ? 

4. Find the amount of poll taxes in your city or town. 

Property is divided into two classes for taxation : — 

(a) Real Estate, regarded as immovable, as land and buildings, 
including mines, quarries, forests, railroads, etc.; and 

(b) Personal Estate, which is usually movable. 

5. Give examples of valuable personal property. 
6. How large a tax on property is assessed in your city or town ? 

Suppose a town has to raise a certain sum of money for the 
expenses of the coming year. Officers, called assessors, first estimate 
the value of the property to be taxed, and then assess each owner in 
proportion to what he has. | 

7. If the amount to be raised is $20,000, and the poll tax 
amounts to $1600, how large a property tax must be assessed ? 


8. The assessed valuation of the property of a certain town is 
$200,000. The tax to be raised is $4000. ‘What is the rate of 
taxation ? 

9. What shall Mr. Smith pay, who owns $5000 worth of prop- 
erty in the town ? 

10. My property is assessed at $3000. The tax rate is 14%. 
What is my tax if I pay a poll tax of $2? 

11. The tax to be raised is $15,000. There are 250 polls, that is, 
male citizens over 21. What must be raised by a property tax if 
the poll tax is $2 each? 


Written TAXES 179 


1. Assessors find the value of real estate in their city to be 
$ 15,000,000, and of personal estate $5,000,000. They assess a tax 
for state, county, and city. If the rate is $15 tax on $1000 valua- 
tion, the total to be collected will be how much ? 

2. The rate is $124 0n $ 1006. What will be assessed on $ 4,000,- 
000 valuation? A man who pays $125 is assessed on how much ? 

3. A man’s tax, including $2 poll, is $122. The rate is 11%, 
or $a on $1000, $y on $1. His property is valued at how much ? 

4. 900 is what per cent of 60,000? If $12 is the tax on $1000, 
what is the tax on $1? What the rate per cent ? 

5. Find the rate when the tax on S Beate 000 is $1770. On $100 
the tax would be $ a. 


Find the rate of taxation on a thousand dollars under the following 
conditions : — 


ASSESSED ‘TAX TO BE RAISED ASSESSED TAX TO BE RAISED 
VALUATION ON PROPERTY VALUATION ON PROPERTY 
6. $48,000 $1600 10. $51,000,000 $8,000,000 
7. $650,000 $ 1300 11. $49,000,000 $650,000 
8. $1,650,000 $110,000 12. $135,000,000 $900,000 
9. $2,470,000 $190,000 1S, $ 215,000 $ 2700 


14. The valuation of property in a certain town is $2,306,000. 
The tax raised on the property is $39,202. What is the rate ? 


15. If I own $6500 worth of property in the same town, what 
will be my tax, including a poll tax of $2? 


16. In the city of B the rate of taxation is $615.50 on a thousand; 
polls, $1.75. If a mill owner’s tax is on $250,000 worth of real 
estate, what is his total tax ? 


17. The taxable property in the town of Pleasant Valley is esti- 
mated at $3,000,000; the number of polls, 1800; the state tax, 
$1044; the county tax, $4500; the town tax, $36,300. If the poll 
tax is $2.75, what must be the rate of property. tax on a thousand 
dollars’ worth of property ? 


180 GOVERNMENT REVENUES Oral 


1. The expenses of the national government are not paid from a 
tax upon property and polls, as are the expenses of the city, county, 
and state, but are paid from : — 


I. The Internal Revenue, chiefly taxes of a fixed sum on the right 
to make or sell spirituous liquors, tobaccos, ete. 


II. The Customs Revenue (tariff, duty), taxes collected on goods 
imported from foreign countries. 
2. What need of money has the government ? 


Notre. The expenses of the government are over $1,000,000 per day. 
3. Mention several articles commonly imported. 


4. Merchandise brought into this country is either : — 
I. On the free list, that is, exempt from duty; or 


II. Subject to an ad valorem duty, a per cent on the cost of the 
goods where they were bought, as shown by the invoice; or 


III. A specific duty, fixed according to number, quantity, weight, 
etc., without reference to value; or 


IV. There may be both an ad valorem and a specific duty. 


5. Find the duty at 15% on 200 T. of coke invoiced at $1.50 a 
ton. Is the duty specific or ad valorem? 

Notre. Invoices are made out in the money of the country where the goods 
were bought. When changed to United States money, the duty is computed on 
the nearest dollar, 50 cents counting as $1. 


Imported goods must be brought to a port of entry, a place where the govern- 
ment has established a custom house with officers for the collecting of the duties. 


6. What is meant by smuggling ? 


7. A gross of leather pocketbooks invoiced at $12.50 a dozen 
pays 30% ad valorem. What is the duty ? 


8. What is the duty on an importation of $5600 at an ad valorem 
rate of 121% ? 


Oral and Written GOVERNMENT REVENUES 181 


Tare, Leakage, and Breakage are allowances for boxes, bags, etc., 
used in packing, and for liquids lost from barrels or bottles, etc. 


9. A dealer withdraws from the custom house 4 T. (2240 lb.) of 
rice, 8% tare. On what weight must he pay duty ? 


10. What will this amount to at 11 a pound? Is this specific or 
ad valorem duty? Why ? 


11. Define gross weight and net weight. 


12. An importation of velvet invoiced at 5181.35 francs weighs 
400 lb.10% tare. Which would be more, a duty $1.50 a pound or 
50% ad valorem? (A franc = $0.193.) 


13. 20 bbl. vinegar of 42 gal. each pay a specific duty of 71¢ a 
gal., leakage 30 gal. Find the whole duty and the per cent of 
leakage. 


14. The duty on cut nails is 221% ad valorem. $183.75, the 
cost including duty on a certain importation, is what per cent of the 
amount of the invoice? They were invoiced at $a. 


15. In 1903 the duty on Brussels carpet was 28¢ a square yard 
and 40% ad valorem. Find the total cost of 200 running yards 
invoiced at 6s. a yard, 3 yd. wide. (1s. = $ 0.244.) 

16. The gross cost of a lot of calfskins is $ 740, including $ 20 
freight and $120 duty. Find the ad valorem rate. 


17. If the cost of gloves is doubled by importing, what will be the 
profit on a pair invoiced at 60 fr. a dozen, and sold for $ 2.25? 


18. Find the duty on 50 dozen rubber coats at £11-per dozen. 
Duty, 40%. (The value of £1 = $ 4.8665.) 


19. What is the duty on 12 dozen suits invoiced at £36? Rate, 
50%. 
20. What is the duty on 3500 lb. cheese at 6 ¢ specific duty ?. If 


the cheese is invoiced at 9%, to what ad valorem duty is this 
equivalent? 


182 COMPOUND INTEREST Oral and Written 


1. Jan. 1, 1904, Mr. Dale borrows $500 of Mr. Coe, agreeing to 
pay 6% interest at the end of every year. How much interest is 
due at the end of the first year ? 


2. Who is entitled, under the agreement, to use this $30 interest 
for the second year ? 


3. If Mr. Dale uses the overdue interest during the second year, 
instead of paying it to Mr. Coe, is it just that he should pay for yee 
use of it? 

4. On how much then should the debtor (Mr. Dale) pay interest 
the second year, including both principal and overdue interest ? 

Interest reckoned on both principal and overdue interest added to 
the principal as often as due is called compound interest. 

Nore. When interest is added to the principal, or ‘‘ compounded,”’ it is done 
yearly, unless otherwise stated, as half-yearly, quarterly, or oftener. 

5. What is due on a debt of $600, which has been standing 2 yr. 
6 mo. 18 da., interest at 6% compounded annually? Explain the 
following process. 


Principal used for lst year. ‘ : ‘ $600 
Interest due at end of Ist year ; : 4 36 
Principal used for 2d year : : : ; % 636 
Interest due at end of 2d year : : : 38.16 
Principal used for 6 mo. 18 da. : : : $674.16 
Interest due at end of 6 mo. 18 da. : : 22.25 . 
Amount due at settlement . ; : ; $ 696.41 
First principal . : : 5 é : 600 
Compound interest ‘ 5 : , $96.41 
Simple interest would have tears : ; 91.80 
Interest on all overdue interest . ; : $4.61 


6. What is due on a note of $1000 standing 3 yr. 6 mo., interest 
due annually at 6% ? 


7. Find the compound interest, that is the amount due less the 
principal, on a note of $800 at 5% that has run 2 yr. 8 mo., interest 
due annually. 


Written COMPOUND INTEREST 183 


1. Find the compound interest of $500 for 3 yr. at 5%. 
2. What is the compound interest at 4% of $ 2000 for 2 yr. 6 mo.? 
3. Interest compounds semiannually on $400, at 8% a year. 


For 1 yr. 6 mo., what is the amount due ? 


Note. Compound interest is not in general use. The collection of compound 
interest on notes and debts cannot be enforced, even when agreed upon; it may 
happen, however, that large investors wish to compute the result of reinvesting 
all interest when due. It is then computed by tables. Savings banks generally 
allow compound interest on deposits. 


COMPOUND INTEREST TABLE 


AMOUNT OF $1 


2, |2 PER CENT 4 PER Cent | 5 PER CENT | 6 Per Cent 


as 
ni 


24 Per Cent | 3 PER CENT | 33 PER CENT 


CoN mH OTP WW KE 


— 


1.020000 
1.040400 
1.061208 
1.082432 
1.104081 
1.126162 
1.148686 
1.171660 
1.195098 
1.218994 


1.025000 
1.050625 
1.076891 
1.105815 
1.131408 
1.159695 
1.188686 
1.218403 
1.248863 
1.280085 


1.050000 
1.060900 
1.092727 
1.125509 
1.159274 
1.194052 
1.229874 
1.266770 
1.804773 
1.343916 


1.085000 
1.071225 
1.108718 
1.147523 
1.187686 
1.229225 
1.272279 
1.516809 
1.862987 
1.410599 


1.040000 
1.081600 
1.124864 
1.169859 
1.216653 
1.265519 
1.315982 
1.868569 
1.423312 
1.480244 


1.050000 
1.125600 
1.157625 
1.215506 
1.276282 
1.540096 
1.407100 
1.477455 
1.551828 
1.628895 


1.060000 
1.102500 
1.191016 
1.262447 
1.338226 
1.418519 
1.503630 
1.593848 
1.689479 
1.790848 


Nore. The compound interest on any amount for 5 yr. at 6% payable semi- 
annually is evidently the same as upon the same amount for 10 yr. at 3 % payable 
annually. 


Find by the table the amount at compound interest of : — 
1. $500 for 2 yr. at 5% ; semiannual dividend. | 
2. $600 for 3 yr. 6 mo. at 5% ; semiannual dividend. 
3. $320 for 1 yr. 9 mo. at 8% ; quarterly dividend. 
4. $ 800 for 2 yr. 4 mo. at 4%; semiannual dividend. 


184 BORROWING FROM A BANK Oral 


One of the sources of income of banks is from lending money. If 
I wish to borrow money from a bank, I give a promissory note. 
(See page 169.) 

A promissory note given a bank is usually in the following 
form : — 


PO5__. Ypsilanti, Mich., Sept. //, 1904. 


Three montha, without quaee, after date, A promise 
to pay to the order of R. W. Mremhrctt, Cashier, 
Sacly-fve Dollars 


at Ypatlant0e Javingy Kank, Ypsilanti, Mich. 
Value received. 

Residence, 3/¥ %. Adame st. Yonn Doe. 
Due, /2///[04. Discount, $0.98. 


According to the custom of banks, the interest (called by the 
banks, discount) on the face of the note is deducted from the face 
when the money is borrowed and the proceeds, that is, the difference 
between the face of the note and the interest, is given the borrower. 


1. If John Doe gives his note for $65 and the interest for the 
time is $0.98, what does he receive ? 
2. At the end of three months what does he pay the bank ? 


3. If Mr. Doe had given his note for $65 to someone, not a 
banker, what would he have received at the time the note was given? 


4. If the interest of this for 3 months had been $0.98, what 
would have settled the note at the end of 3 months? 


5. The rate being the same, how did the interest compare. in each 
case ? 


6. How much money had Mr. Doe the use of in each case ? 


Oral BORROWING FROM BANKS: BANK DISCOUNT 185 


1. I borrowed $100 of a bank. I gave my note due in 6 mo. 
without grace. Rate of discount (interest) is 6%. 
How much money did I actually get at the bank ? 
What did I pay at the end of 6 mo. ? 


2. How much more money could I have hired for $3 of some 
one not connected with the bank ? 


3. State the difference between bank discount and interest. 


4. What must be done before Mr. Alden can transfer the owner- 
ship of the following note to a third person ? 


$500... Milwaukee, Wis., Aug. /2, 1903. 


Jwo montha after date 4 promise to pay to the 
order of 
Sive /tundred 
at the Shurd ational hank. 


Value received. /¥orattvo. Long. 


5. What responsibility does the indorser of a note assume ? 
6. In what case may Mr. Alden be called upon to pay this note? 
7. What risk does a bank take in buying this note of Mr. Alden 
if he is a reliable person ? _ 
8. When does this note mature or become due, no grace being 
allowed ? 
9. Under what conditions will it draw interest ? 
10. What is this note worth Oct. 12,1908? Oct. 15, 1903 ? 
11. Why is it not worth $500 at date ? 


12. How much could Mr. Alden get at the Third National Bank 
for his own note, that is, one of which he is the maker, of $500 due 
in 2 months, the rate of interest charged by the bank being 6% ? 


186 BANK DISCOUNT Oral 


18. Why should Mr. Alden receive from the bank just as much 
for a note which he has indorsed as for one in which he is the 
maker, if it is to run the same time and is worth the same at 
maturity ? 

14. What will the Third National Bank pay for this note on 
Aug. 12, 1903? |The rate of interest charged by the bank is 6%. 


15. When does the bank get back the $495? How much more 
does it get on Oct. 12, 1903 ? 

Should Mr. Long fail to pay the note before the closing of the 
bank on the day of maturity, immediate notice is given the indorser 
and he is held for payment. 

Whether you are the maker or indorser of a note given to a 
bank, the transaction is called selling or discounting the note, the 
interest is called bank discount, and what you receive for it is the 
proceeds. 

Written 


Most of the notes discounted at banks, or by brokers or others, are 
given for short times, 30, 60, 90 days, or 2, 3, 4, or 6 months. 

Norr. Compute bank discount as if it were interest on the face of a note 
for the time the bank’s money is used; and take the shortest method. Allow 


three days of grace if such is the lawful custom in your state. Answers are 
given both with grace and without it. 


1. What will a bank pay me for a note of $800 payable in 3 mo., 
the rate being 43% ? 


2. How much of its money will a bank permit me to use in 
return for a note of $720? Money is worth 5%, and the note runs 
60 days. 


38. What allowance shall Mr. Strong make to the Exchange 
Bank for its prepayment of a 4-mo. note for $875 at a discount rate 
of 3% ? 


The term of discount is the time for which the bank’s money is 
used. It extends from the day of discount to the day of maturity. — 


BANK DISCOUNT 187 


Find the bank discount and the proceeds of notes made under these 
conditions, and discounted ut date : — 


TIME RATE OF TIME RATE OF 
FACE To Run DIscouNntT FAcE To Run Discount 
1. $525 30 da. 6% 4. $800 90 da. 71% 
Ze h Huii oon O: ALG, 5. $960 60 da. 4% 
38. $324 6,mo. 8% 6h (2lin Fo da. BL 


When a note is discounted at date, the time named in the note 
(with grace or without, as the case may be) is the term of discount, 
showing how long the discounter’s money is used. <A note, however, 
nay be sold or discounted at any time between date and maturity. 


The term of discount extends from day of discount to the day of 
maturity. 

Nort. The method of reckoning the time from the day of discount to the 
day of maturity is not uniform among banks. 

The two more common methods are the following : — 


I. When the time is less than two months, the exact number of days is 
counted ; but when it is more than two months, the time is reckoned in months 
and days. (See page 151.) Or, 

II. The exact number of days is taken in all cases. 

In general, the latter method is used, when notes are large, being to the 
advantage of the bank. 

Thus, a 4-month note dated June 30 matures, grace allowed, Nov. 2. If dis- 
counted July 10, interest may be computed either for 115 days or 3 mo. 23 da., 
the difference being $384 in favor of the bank on a $10,000 note. 

The student should conform to the custom of his own vicinity. Answers to 
examples are given for both methods. 


Find date of maturity and term of discount by each method : — 


DATE OF TIME DAY OF DATE OF TIME Day oF 
NotTE to Run DIscountT NOTE To RuN DISCOUNT 


May8 60da. June10 5. Aprill4 4mo. June8 
Nov.17 90da. Dec.14 6. Jan. 25 30 da. Jan. 29 
Avexommmearmos, Anger 297617. Septarovni4: mon i Noveld 
Mar.17 3mo. Mayl 8. Feb. 10 90 da. Mar. 6 


PO ~D 


188 BANK DISCOUNT 


Notes discounted after Date 


1. I get a 3-mo. note discounted 27 days after date. What is 
the term of discount ? 


2. What if it were sold 24 days before maturity ? 
3. A 6-mo. note for $450 dated Aug. 11 is discounted Sept. 4, 
at 6%. Reckon months and days with grace. Find proceeds. 


4. A 90-da. note for $ 1000 is discounted 37 da. before maturity. 
Find the proceeds, the rate being 5%. 


5. A 5-mo. note for $800 was sold at 3% discount 80 days after 
it was made. Proceeds without grace ? 


6. 60 days; $450; 4%; date June 15; day of discount July 1. 
What does the borrower have for immediate use out of his note? 


Using these data, find the proceeds of notes. Conform to the custom 
of your own vicinity in allowing grace and finding the term of discount. 


FACE DATE TIME DATE OF DiscouNT RATE 
7 $875 Jan.16,°03  90da Feb. 24,703 5% 
8. $984 Aug. 8, ’04 5 mo. Oct: 27, °04 6% 
9. $696 June 15, ’08 60 da. Aug. 4, 708 8% 
10:: $842.50). « Oots31, 02, 55 demo, Nov. 1, 02 54% 
11. $1250 July 9, 704 60 da. Aug. 29,704 41% 


Notes that are discounted commonly bear no interest. When an 
interest-bearing note is discounted, the maturity value of the note must 
be made the base of discount. 


1. An interest-bearing note of $1000 is payable 1 iniyr. Interest 
8%. What is it worth at maturity ? 


2. This note is discounted at a bank 3 months before maturity at 
6%. Find the proceeds. 


Sucegstion. Find the proceeds on $1080. Why ? 


Written BANK DISCOUNT EXERCISES 189 


1. A 4-mo. note for $1200, drawing 9% interest, is discounted 
at 4% 3 months before maturity, without grace. Required the 
proceeds. | 

2. Face, $500; rate of interest, 5%; time to run, 60 da.; term 
of discount, 48 da.; rate of discount, 6%. Proceeds ? 

3. A 90-da. note for $720, dated May 15, 1904, drawing 8% 
interest, is discounted June 12, 1904, at 6%. Proceeds ? 

4, Write an interest-bearing note and find the proceeds. 

5. Sold a $400-note to the Merchants’ Bank at 8% discount. It 
had 40 days to run. Proceeds? 


6. What shall the Farmers’ Bank pay for a note of $1000; the 
rate of discount is 7%; the note matures 4 months from April 10, 
1904, and is bought 25 days after date ? 

7. An interest-bearing note for $1200 is payable in one year 
from date. What will pay it at maturity ? 

8. If this note is discounted 6 months before maturity at 5%, 
what are the proceeds? 

9. What will it bring if sold to a bank at 6% discount when it 
is 3 months old ? 

10. What will the same bank pay for it at date ? 


11. A bank bought a $600 note for $591. What was the rate of 
discount if the note had 60 days to run ? 


Find proceeds of notes under these conditions, each bearing 6% 
interest. 
FAcE RATE DATE OF NOTE RuNS DISCOUNTED 


12. $450. 4% May10,’03 60da. 28 da. after date 

13. $720 5% Aug.15,’04 90da. 48da. before maturity 
14. $958 7% Oct.12,’04 45da. at date 

15. $800 5% Aug. 21,705 90da. Oct. 1, ’05 

16. $278 8% Dec. 20,’04 3mo. 16 da. after date 

17. $5000 3% <Aug.19,’04 60da. Sept. 19, ’04 


190 STOCKS Oral 


When a business requires more capital, or money invested, than a 
single individual or a few partners wish to furnish, a stock company, 
or corporation, may be formed with any number of partners, who 
choose a board of directors to conduct the business as one person. 

The capital stock of a stock company is divided into shares of a 
fixed amount, usually $100. The value of the shares in different 
corporations varies, and is determined by the persons forming the 
corporation. 


1. A corporation is formed with a capital of $250,000, shares 
$100 each. How many shares are there ? 


2. If there were only 500 shares, what would be the value of 
each ? | 


Each owner or stockholder receives a certificate of stock bearing the 
seal of the corporation and giving the number and size of the shares. 
Since shares are often sold, stockholders are often changing. 


Stock Certificate 


Incorporated under the Laws of the State of New York. 


No. L/2, /2 shares. 
EASTERN PACKING COMPANY. 
Ohis certifies that 
is the owner of 
Hundred Dollars each of the full paid Capital Stock of 
the EKastern Packing Company. 


Transferable only on the books of the company in person or by attorney upon 
surrender of this certificate. 


New York, Yuly 12 Loo. 


Carl Jacobs, Nn. S. Kendatt, 


Secretary. President. 


Oral STOCKS 191 


1. From whom does the Eastern Packing Company get the right 
to carry on business as a corporation ? 


2. Who is the owner of the certificate ? 


8. What is the face value of each share ? 


The income or profit of the business is called a dividend, because it 
is divided and paid yearly, half-yearly, or quarterly to the stock- 
holders as a per cent on the par value or face value of each share; that 
is, the value named in the certificate of stock. 


4. About what income does one receive from $100 loaned on an 
interest-bearing note ? 


5. If the yearly dividend on a $ 100. share in a gas company is 
$ 20, which would you prefer, stock in the company, or to loan your 
money ? 


6. Could you afford to give more than $100 for a share in such 
a company ? 
When a business is prosperous and. paying large dividends, the 
stock usually sells above par, and is then said to be at a premium. 


7. Which would pay you the better income, money loaned at 6% 
interest, or stock paying an annual dividend of $4 on a share ($ 100) ? 


8. In that case could you afford to pay par value for the stock ? 
Stock selling below par is said to be at a discount. 


9. I own 10 shares ($100 each) of mining stock. The company 
declares a 10% dividend. What is my share? 


10. If such a dividend is declared semiannually, to what rate of 
interest is it equivalent ? 


11. What will three $100 shares of railroad stock cost at a 
discount of 10%? At a premium of 20% ? 


12. Bought 5 shares of mill stock at 103 and sold it at 108. 
What did I gain? 


13. Would one care to buy stock at 97% discount ? 


192 STOCKS Oral 


A company may issue two kinds of stock, viz: — 

Preferred stock, which entitles the holder to dividends which are a 
certain per cent of the par value of the stock held; and 

Common stock, which entitles the holder to a share of part or all 
of the remainder of the gains. 

Sometimes an assessment is levied on the stockholders to pay the 
debts of the company. 

Look up stock quotations in some newspaper. 

A newspaper quotation of 165 means that $100 of stock, that is, 
stock whose par value is $100, is selling for $165. 

Stock is usually bought and sold through a stock broker who belongs 
to some stock exchange. ‘The usual brokerage charged is 1% of the 
par value, or $0.121 for buying 1 share of $ 100 stock. 


1. Stock quoted at 120 will cost you what if you buy through a 
broker ? 
2. When stock is selling at 15% below par, what is the market 


value, or at what is the stock quoted ? 


3. I buy 10 shares of railroad stock quoted at 104%, brokerage 4. 
What do they cost me ? 


4. I own 20 shares in a paper company. What do I get for them 
if I sell direct (i.e. not through a broker) at 108? 


5. I received $80 dividend on stock paying an 8% dividend. 
How many $100 shares have I? 


6. If stock is selling at 200 and paying a 25% dividend, what 
rate of income is this? 

7. How many shares of 5% stock will yield an annual income 
of $1000? 

8. A broker receives $20 for a sale of stock. How many $100 
shares were sold ? 


9. The market value of a $50 share of stock is $65. What is 
the per cent of premium ? 


Oral STOCKS 193 


1. 15 boys organize a ball club with a capital of $120. What 
does each boy contribute if they share equally ? 

2. Suppose this capital is divided into 25% shares, how many 
shares will there be ? 

3. Tom Jones, the captain, takes 80 shares at par. What is the 
value of his stock in the club? 

4. After the members of the club have subscribed for all the 
stock they care to take, 16 shares remain. They are bought by an 
outsider at 10% above par. What does he pay for them ? 

5. Harry Irving, one of the original stockholders, is obliged to 
retire from the club, and sells his stock to the catcher at a discount 
of 15% from par. He had 8 shares. How much did he lose by his 
investment ? 

6. At the end of the season, $40 remained in the treasury, over 
and above expenses. ‘The club voted to divide this among the stock- 
holders in proportion to their holdings. Ed Sprinter had 16 shares. 
What was his part of the dividend ? 

7. The next season the club started out by levying an assessment 
of 162% for an outfit. What was paid on each share ? 

8. An electric railroad pays a semiannual dividend of 4% on 
$5,000,000 of capital. What is the annual dividend ? 

9. What will the market value of the stock be at 20% premium ? 

10. Bought 10 shares of Pennsylvania Railroad stock at 75, and 
brokerage of 4. What was the cost ? 

11. Sold 20 shares of stock in the Massachusetts Mills at 1064. 
I bought it for 105. What was my gain ? 

12. Bought telephone stock at 120, and received an annual divi- 
dend of $8. What per cent of the par value was this ? 

18. Which is more profitable, to buy stock at 80 and sell it at 90, 
or to buy it at 150 and sell it at 175 ? 

14. A mining stock pays 12% annually. My dividend is $240. 
How many $100 shares of the stock do I own ? 


194 STOCKS Written 


1. What is the market value of 35 enone of North Western 
stock at 483% above par ? 


2. What would be the value of the same stock if sold at the 
same rate below par ? 


3. I receive a stock dividend of $1728. This is at the rate of 
142% on the par value of my investment. How much of the stock 
do I own? . 


4, A man exchanges 170 shares of stock worth 103 in the market 
for a cottage at the seaside valued at $8510. The difference was 
made up in mill stock at a par value of 50 per share. How many 
shares were there? Leave brokerage out of the account. 


5. An optimist bought 1200 shares of Texas Oil stock at 115, 
and was glad to sell it at 58. What did his experience cost him ? 


6. The Atlantic Steamship Company is capitalized at $8,000,000. 
The receipts for the year are $16,400,000. The expenses are 
$ 14,800,000. $600,000 is put into a reserve fund, and the remainder 
distributed as a dividend. What rate per cent of dividend was 
declared ? 


7. How many hundred-dollar shares of mining stock can be 
bought at 118 for $3750, and what sui will remain? (Parts of a 
share are not sold.) 


8. I receive $2133 as the net profits of stock bought at par and 
sold at 107. How many hundred-dollar shares were sold, allowing + 
brokerage ? 


9. My broker paid me $8595 which he had received for Old 
Colony railroad stock sold for me at 4 brokerage. How many shares 
did he sell at 215? 


10. In the New York stock market 50,000 shares of railroad stock 
were bought at a premium of 227, and sold the next day at a premium 
of 26%. The brokerage in each case being 4, required the profits. 


Oral BONDS 195 


When corporations, or national, state, or city governments, borrow 
large sums of money, they usually give a series of bonds, or promis- 
sory notes, for one or more hundred or thousand dollars each, and to 
run several years at a fixed rate of interest. Instead of finding 
some one that will lend the money needed, the bonds are issued and 
offered for sale. 

Registered bonds are recorded by number on the books of the cor- 
poration with the name and address of the holders. They can 
change owners only through the office of the treasurer. The interest 
is sent to the holder when due. 

Coupon bonds bear small, detachable coupons or certificates of 
the amount of in- 
terest regularly due. 
These coupons are 
paid by the treas- 
urer on  presenta- 
tion, or they may Will pay to bearer at the office of the 
be deposited at | Company Dollars 
one’s bank for col- 
lection. 


One of several interest coupons attached to a bond. 


The Northern Loan Association 


OF ST. PAUL, MINNESOTA, 


on the._./5_..day of ...dfrtt..., 1904, 


being one year’a interest on coupon 


1. If this coupon 
is attached to a7% bond No. /37. 


bond, what is the Gdward Yamen, 
face value of the Secretary. |. 


bond ? 
2. When is the next payment of interest due ? 


3. Where can it be collected, and by whom ? 

4. If the bonds sell at 140, what would this one cost ? 

5. What would the annual rate of income be ? 

6. My 44% bonds yield me $180 annually. What is their par 
value ? 


7. I get only 3% on what I paid for them. At what‘were they 
quoted when I bought ? 


196 BONDS Oral 


1. I receive an income of $200 from 4% bonds. What is their 
face value? 

2. I receive $30 each year as interest on a 6% bond. What is 
its face ? 


3. I wish to secure an income of $1200. How much shall I 
spend for 4% bonds at par to do this ? 


4. The semiannual coupon of a government 2% bond is worth 
$50. What is the face of the bond ? 


5. A father gives his son sufficient 5% bonds to pay his college 
expenses with their income. His expenses amount to $800 a year. 
What is the face value of the bonds ? 


6. I receive $36 a year as interest on bonds whose face value is 
$600. What is the rate of interest ? 


7. If a five-thousand-dollar bond yields $250 annually, what 
must the rate of interest be ? 


8. $75 is the interest on a thousand-dollar city bond. What per 
cent does the investment pay ? 


9. Which pays the larger rate of interest, a thousand-dollar bond _ 
that yields $50 annually, or a five-hundred-dollar bond that yields 
$12.50 semiannually ? 


10. If a 5% bond pays $75 annually, what will a 6% bond of 
the same size pay ? 


11. Bought a U.S. bond for $540, and sold it for $630. What 
was my per cent of profit ? 


12. A coupon evidently cut from an 8% bond called for the pay- 
ment of $40 interest. If the interest was payable semiannually, 
what was the face of the bond ? 


13. A bankrupt corporation pays 70% of the face value of its 
bonds. I hold $3500 worth. What shall I lose? 


Oral and Written STOCKS AND BONDS 197 


1. I receive $5 on a hundred-dollar bond that cost me $ 80. 
This is ,% of the investment, or a per cent ? 

2. What rate of interest does a 4% bond pay when bought at 
pat? Does it pay more or less if bought below par? If bought 
above par ? 

3. What rate of interest would a 4% bond pay if bought at 200? 
At 50? <At120? Ati110? At1074? 

4. Which pays the greater rate of income, a 4% bond bought at 
par, or a 3% bond bought at 60 ? 

5. Bought a 5% bond at 105. What per cent did I secure on 
my investment ? 

6. I traded 50 shares of manufacturing stock listed at 1081 for a 
five-thousand-dollar bond which is selling in the market at 1093. 
How much did I gain or lose ? 

7. Paid $ 640 for a hundred-dollar share of copper stock which 
paid quarterly dividends of 12%. What per cent did I secure on my 
investment ? 

8. Sold $6000 of the bonds of a bankrupt road for 183. I bought 
them at par and received no interest. What did I lose on that 
investment ? 

9. Which is more valuable, an 8% stock at 200, or a 6% bond at 
150? 

10. Bought 6 thousand-dollar bonds at 108? and 4 brokerage, and 
sold them for 1123 and brokerage 4. Required my gain. 

11. Sold 90. shares of insurance stock at 98, and with the proceeds 
bought mining stock at 110. How many shares did I buy, and how 
much money remained ? 

12. A thousand shares of Calumet and Hecla stock bought at 118 
are sold at a premium of 841. The gain per cent is a. 

13. I am offered either $1500 cash or 7 shares of 8% stock whose 
market value is 220, for 15 shares of P. W. & B. stock. Which is 
the better offer, and how much ? 


198 EXCHANGE: POSTAL MONEY ORDERS: CHECKS Oral 


Payment at a Distance without sending Money 


1. If you should send to the Peoria Bicycle Company for a 
bicycle, in what ways could you send the payment ? 


2. Mention some objections to sending coin or paper money by 
mail or express. ; 

The postal service and some express companies keep large sums 
in many offices. If you pay from $1 to $100 to a postmaster or 
express agent, he can write an order directing the postmaster or agent, 
at another office to pay the same sum to any person you name. For 
this accommodation you pay him from 3 to 30 ¢, no matter what the 
distance; or, if you send toa foreign country, from 10 ¢ to $1. This 
is the cost of exchange. 

Norte. Post-oftice orders are payable at an office named ; express orders, at 
any office of the same company. 


The charges for postal money orders payable in the United States 
are as follows : — 


Not over Si c00 Rel ie PA ae eee Over $30.00 to $40.00 . . . . 15¢ 
Over $ 2.50 to! 6.00 iio. oe Ps Over” 40.00 tos 50.00 Ne) vente 
Over 5.00 t0 10.00 4 2. 1 2°82" Over” 60.00'to: “60,00 =) eo 
Over 10.00 to'20.00''..) J) 2 10% |" “Over® 601006" "75.00" et ae aeeae 
Over 20,00 to 30.00. . -. .....12%, Over °75.00 to 100.00) ao 


Norn. The maximum amount for which a single money order may be issued 
is $100. 

3. What will it cost me to send $70.50 to Mandell Bros., Chicago, 
including the cost of the money order ? 


4. I buy some books in New York. The cost is $7.35. What 
will a money order cost me ? 


5. What must you pay in New York for an international money 
order for 200 m. payable in Hamburg, the rate being 10 ¢ on each 
$10 or fraction of $10? A mark = $0.288. 


If a person, say Edward Bacon, keeps his money deposited at a 
national bank, or with a banking company, he may write a check for 
payment as on the next page : — 


Oral EXCHANGE: CHECKS 199 


Chicago, uly /2, 1904. No. dhe. 


State Wank of Chicago 


LA SALLE & WASHINGTON STS. 
Pay to the order of____- Simmonds ¥ Sewton 
, 2h 
Atnely-erghnl F 9 


6Gdward Bacon. 


Simmonds & Newton, on receiving this check will indorse it; 
that is, sign the firm name “ Sim- 
monds & Newton” across the back, cia eon 
and deposit it at the bank with 
which they are doing business. | Mmmonda ¥ Sewton. 
The bank will then collect the 
amount, usually without charge to 
a regular depositor. If one has no 
bank account, a small fee of 10¢ Ean aas 
to 25¢ is generally charged for 


collecting. This fee is called the 


exchange. Indorsed in full 
If Simmonds & Newton “indorse 
in blank,” that is, simply sign their Say to the order of 
name, the check may be collected fame Hay. 
in Chicago by any one known to 
the State Bank of Chicago. HAmmonds ¥ Sewton. 
iPeitealiemincaorsed, sin. tulktias, 


“ Pay to the order of James Gray, 
Simmonds & Newton,” it may be james Gray: 
paid to James Gray or his order as 


soon as he indorses it. 
Most debts are paid in this way. 


200 EXCHANGE: DRAFTS Oral 


If a party, say Howe & Co., of Albany, cannot draw a check, or if 
the creditor, E. L. Harris & Co., in Syracuse, will not accept one, a 
draft (a banker’s check) may be bought at a bank, for a small cost of 
exchange, like an order at a post office. Thus: — 


PI2dSH.__ Albany, Yuly LEN LIGE: 


Tenth ational Bank 


Pay to the order.of rower i Wonks oe 


Iwo /~undred thirty-four yl SEL See ae Os eee eee Dollars. 
To the 
Farmer’ Sationat Bank, 
Syaewe, cS. yy. Salrick Matthews, 


Cashier. 


1. Of what bank is Matthews cashier ? 
2. Where is the draft payable? 
3 


. How can Howe & Co. make it payable to other creditors ? 


4. Make a draft from the National Exchange Bank of Peoria to 
the Traders’ Mutual Bank of Chicago. The Western Machine Co. 
pays $400 for it. 


5. Why is a bank draft more likely to be “good” than a private 
check ? 


Notr. A bank draft on New York may be cashed almost anywhere in the 
United States. Drafts on another city will usually be paid before collection in 
the region of which it is a commercial center. 

6. If Howe & Co. are going to mail this to E. L. Harris & Co., 
why should it be “indorsed in full” ? 


7. If Howe & Co. prefer, they can have the draft made payable 
to HK. L. Harris & Co. Why is the first plan better ? 


DRAFTS: COLLECTING MONEY THROUGH A BANK 201 


A great deal of the collecting of debts is done through banks by 
what are called commercial drafts. 

Suppose Haines & Co., of Topeka, has bought goods of 8. T. 
Richards & Co., of Chicago, and has not paid the bill when due, say 
30 or 60 days after the goods were bought. Richards & Co. may 
make out a draft as follows and deposit it with their bank in Chicago 
for collection. 


No. 34665, Chicago, Ill., Nay 6, 1904. 


At sight pay to the order of 
Si he Si tate Kank of Chteago 


Shree /tundred Forly-etght 


To /fainw ¥ Eo., 
Topeka, Kaw. Sp, ST. Reharda ¥ Go. 


The Chicago bank now sends this draft to some bank in Topeka. 
The Topeka bank sends a messenger to Haines & Co. and presents the 
draft for payment. 

Haines & Co. either write across the face, “accepted,” with the 
date, and firm’s signature, or they refuse to pay it. 

In case they refuse to pay it, the draft is returned to the State 
Bank of Chicago and Richards & Co. are notified. They must now 
take other means of collecting. 

The form shown here is that of a sight draft. If “Thirty days 
after date,” or some time is written in place of “at sight,” the draft 
becomes a time draft. 

When a draft is accepted it then has the same force as a promissory 
note owned by the payee and may be discounted at a bank as any 
promissory note. 


1. Name the maker, the payee, and the drawee of the draft above. 


202 DRAFTS: COLLECTING THROUGH BANKS 


1. Suppose the draft on the preceding page to have been a 60-day 
time draft and to have been accepted May 10. What is the day of 
maturity and how long has the draft to run before due ? 


2. If sold on the day of acceptance at 6% discount, what are the 
proceeds? (Remember that when accepted it is Da a 
promissory note.) 


3. The bank at Topeka will likely charge a small fee for collect- 
ing the draft. If they charge +% (of the face of the draft) for 
collecting (exchange) and discount it on the day it is bought, what 
shall they remit the State Bank at Chicago ? 


4. F. Alton of New Orleans draws at sight on R. Fay of Waco, 
Tex., Aug. 3, 1903, for $500. Make the draft. 


5. Suppose the debt not due till Nov. 1. Make a proper time 
draft dated Aug. 3. 


6. If discounted Aug. 18, the proceeds would be $a. 


7. If discounted Aug. 3, less an additional 4% for exchange, the 
proceeds would be $y. 


8. Paine of Macon, Ga., owes Drew of Atlanta $4000, due Jan. 1. 
Paine accepts a draft Oct. 1 and discounts it himself for $ a. 


Sight or time drafts if known to be “good” may be sold to a bank 
by allowing a percentage for cost of exchange. 


Thus the State Bank of Chicago might have bought the draft on 
the preceding page of Richards & Co., and ae them a fee of say 
4% for collecting. 


9. A Charleston bank buys a draft on Richmond for $ 2100, 
charging 4% for exchange. If it had taken the draft for collection 
only, the charge would have been 25%. To the maker what is the 
difference in money? In which case is payment made more quickly? 


10. Write a draft of which you are the maker, your teacher the 
payee, and a neighboring bank the drawee. 


Written REVIEW EXERCISES - 2038 


1. (171)? —V361 = 10% of what ? 


2. How much pays for 
of yd. silk at $ 2.50; 
2 pr. blankets at $ 7.374; 
10% otf to the trade and 2% for cash? 


3. Add horizontally : 3.75, 23.08, 176.97, 0.838, 12.374. 
4. $156.91, $73.99, $ 1439, $76.84, $972, $42.97, $ 1982. 


5. I bought a bill of goods-invoiced at $3850. I received two 
discounts of 10% and 5% each. Find the net cost including $13.40 
freight. 


Find cost, but write only the products for adding : — 


6. 162 at 80¢ 8. 901 at 25¢ 10. 11 at 20¢ 
48 at 662 ¢ 1200 at 75¢ 1,8 at 3871 ¢ 
75 at 121 12 at $ 1.162 43 at 25¢ 
24 at 621 ¢ 39 at $ 2.334 100 at 27 ¢ 
871 at 10¢ 42 at 831¢ zy at $1.25 

7. 6400 at 871 ¢ 9. 22 at 21¢ 11. 35, at 90¢ 
279 at 111 ¢ At at 50¢ 48 at 183 ¢ 
108 at 81¢ zi, at $ 1.00 1000 at 27 ¢ 
144 at 61¢ 103 at 28¢ qi at $ 2.50 
1608 at 331¢ 161 at 331¢ 14, at 874 ¢ 


Find total interest due on five notes, as follows. Write only results 
for adding :— 


La. 13. 14, 
$ 500, 24 yr., 4% $720, 45 da., 6% $ 700, 4 yr., 44% 
$ 630, 60 da., 8% $ 376, 30 da., 3% $ 300, 90 da., 6% 
$ 180, 30 da., 12% $ 200, 12 da., 4% $ 400, 63 da., 3% 
$900, 4 mo., 9% $ 820, 10 mo., 6% $ 480, 24 yr., 5% 


$ 200, 15 da., 6% $ 1800, 10 da., 4% $150, 54 da., 6% 


204 REVIEW EXERCISES Written 


1. Estimate the commission on a sale of $5000, at 5%. 


2. Insured a mill, valued at a quarter of a million of dollars, for 
$200,000, at the following rates for 5 years: $50,000 in each of 
three companies, at 3%; $20,000 at 8% ; and the remainder at {%. 
What per cent of the value of the property is my annual premium ? 

3. $40,000 is to be raised by taxation for building a schoolhouse. 
The assessed valuation of the town is $6,400,000. My property is 
assessed at $24,000. What shall [ pay towards the cost of the 
schoolhouse ? 


Find proceeds of notes without grace : — 
4. $ 60,3m0.,8%. 6. $850,47da,4%. 8. $1900, 63 da., 4%. 
5. $260,90da.,6%. 7. $946, 62da.,3%. 9. $1217, 14da.,8%. 


10. Imported 40,000 lb. sugar invoiced at 23 ¢, at 40% ad valorem, 
and 1¢ per pound, specific. Required the cost of the importation. 


11. Bought 19 shares of 7% manufacturing stock, at 1283. 
Received a semiannual dividend, and then sold for 126. No broker- 
age. My gain or loss? 


12. Sold $50,000 worth of hides at 2% commission, and with the 
net proceeds bought cotton at the same commission. Required my ~ 
total commission. 


13. Bought 500 tons Franklin coal at $5.624. Sold at an aver- 
age advance of 22%, but lost 5% in bad debts. Required net gain. 
Allow 25¥¢ a ton storage, and $32.60 for other expenses. 


14. A 6-months’ note for $500, bearing 6% interest, is discounted 
at a bank 40 days before maturity. Required the proceeds. 


15. Invested $5000, in stock paying 5%, at par value. I bor- 
rowed the money at 35%. What was my annual gain? 


16. A dealer sold a piano for 25% less than his asking price and 
yet made $100, or 20% on the cost. Required the cost. 


Written REVIEW EXERCISES 205 


1. The rate of postage to publishers is 1? a pound. If The 
Century averages 11 pounds per copy, what will be the postage bill 
for a month if 90,000 copies are mailed at this rate ? 


2. If wine contains 74% of alcohol, how much alcohol in 6 dozen 
quart bottles that are 6% short of full? 


8. The price of silver Nov. 22, 1902, in London was the lowest 
on record, 2234. d. per ounce. What was Ne per troy pound in our 
money ? Take English money at par. 


4. $18,000,000 New York Central 34% bonds were sold by J. P. 
Morgan & Co. at 1063. What was the total premium? What is the 
total and annual income? What per cent of income do they yield 
at this rate ? 


5. Hired $50,000 at 5% simple interest for 3 years and 6 months. 
I loaned it at 44% compound interest. What did I gain or lose by 
the transaction ? 


6. In the Battle of Gettysburg the Union army lost 23,000 men, 
16,500 of whom were either killed or wounded. What per cent of 
the loss were taken prisoners ? 


7. Gained 28% by selling a coach at $640. What per cent 
should I have gained, if I sold it for $728 ? 


8. I gained $1110, and this was 37% of what I lost on another 
transaction. Required the net loss or gain. 


9. The gross income of the Prudential Insurance Company is 
$126,000. If the average premium upon the risks taken during the 
year is 223%, what is the face of the policies which the company has 
written during the year ? 


10. The price on a certain quantity of standard furniture, as 
quoted by J. H. Harper, amounts to $546.84, 20% and 6% off; and 
as quoted by H. A. Warner & Co., $575.30, 25% and 10% off. Which 
is the better offer and how much ? 


206 PROPORTION: AN EQUALITY OF RATIOS Oral 


1. What is the ratio of 3t05? This ratio may be written 3+5; 
$51 OLD 10; 
Two equal ratios will make a proportion. ‘Thus :— 


P25 a1 LO ie 0:20 =6: 24 
or 12 = 16 j ges a — 6 
3 4 20 24 


The four numbers are said to be in proportion, and are read “12 is 
to 3 as 16 is to 4,” or “the ratio of 12 to 3 is equal to the ratio of 16 


to 4.” 
Test the following proportions to see whether the ratios are equal : — 


2.0 4.0'e= oy A, Bye eens 

3.02 Ve DOR LZ, WAZ etO ier, 

Ay Ot si bs 8. 2% :4% =124% :25%. 
5. 21:5=41:9. 9. 3yd.:4 yd. = $0.75: $1.00. 


The first and last terms of a proportion are the extremes; the second. 
and third terms are the means. ‘The first term in a ratio is an ante- 
cedent and the other a consequent. 

10. Which terms are dividends? Which divisors? Which may 
be numerators? Which denominators? 

11. Arranging the proportion 16:8 = 10:5 in a fractional form, 
we have 18 = 12; multiplying both sides of this equation by 5 x8 or 
40, we have 16 X 5=10 x 8. 

What terms are 16 and 5? Which are the means ? 


12. What conclusion may we draw from Exercise 10? 
Principle. Jn a proportion, the product of the extremes is equal to 
the product of the means. 


13. At least one pair of the ratios must be abstract numbers be- 
fore we may apply this principle. Why is this ? 


Notre. All the terms of a proportion may be expressed as abstract numbers 
for 5 ft. +2 ft. =3 or 5+ 2. 


14. Write the proportion in Exercise 8 in abstract terms. 


Oral and Written PROPORTION 207 


15. Test the proportions in Exs. 1-8 by the principal on page 206. 
16. Find the values of « (make use of the principle on page 206) :— 
Soe ex Scat ELS TalLG els 
Dexaes —= 0° x0 Lay DO siLen ve ©: 246272 
17. How is a missing factor found? How is the missing term of 
a proportion found ? 


Find the missing term in these proportions : — 


DS het (ee OU emer, 24. $0: $9=60 lb. : 27 lb. 
19; 27: a2= 81: 100: 25. 10 T.:4 T.=$~a: $3.75. 
20. «: 16 =130 : 26. 26. 15:¢=3:12, 

Zhe SPREE ees ee ae PATRON ee Le aR aridlh atm 
Boi a 8 16. 28. 91:164=—38:2. 

23. $90: $48=15 yd.: a yd. ROUIE ZOO) ies U2, 


30. Why must the terms of a ratio be hike numbers? 


Since the principle of proportion may be applied to the solution of 
problems in which three terms are given to find the fourth, the sub- 
ject is sometimes called the “ Rule of Three.” 


‘Written 
1. If 16 yards cost $40, what will 10 yards cost? 


EXxpLaNaATion. Since the ratio of their costs 
PROCESS must be equal to the ratio of their lengths, or 
16:10=$40:$a since their costs are proportional to their 
5 5 lengths, we have the proportion. The question 
then is to find one of two numbers when the 
$a2= 10x 940 _ gor product is known. Write the dividend above 
the divisor, and use cancellation. Since the 
p cost is wanted, we write the abstract ratio of 

their lengths. 


2. When 60 bushels of oats cost $36, what will 25 bushels cost? 
3. What will 18 tons of hay cost when 7 tons cost $147? 


208 PROPORTION Written 


1. If 14 men can doa piece of work in 9 days, how long will it 
take 3 men ? | 


3:14 =9 days: x days. 2. Does the time required to do a 

3 piece of work increase or decrease as 

ape 9 days _ go days. the number of workmen increases or 
3 decreases ? 


3. What is the ratio of 14 men to 3 men? 


4. What is the ratio of the time of 14 men, or 9 days, to time of 
3, or 42 days ? 
Since the time decreases as the number of men increases, a propor. 
tion of this sort is called an inverse proportion. 


5. 27 men build a bridge in 12 days. How long will it take 36 
men to build it? What is the ratio of 27 to 36 ? 


6. In the Boer War a town was garrisoned by 2100 men, who had 
provisigns for a 9 months’ siege. How long would the provisions 
last, if they should receive a reénforcement of 600 men ? 


7. 2% dollars is paid for 4¢ bu. oats. What will 194 bu. cost ? 
8. When 33 tons cost $ 27.50, what will 43 tons cost ? 


9. A certain piece of work was to have been performed by 288 
men in 72 days. A number of workmen having been taken sick, 
108 days were required. How many men were taken sick ? 


10. The ratio is 22; the first term, 4 of 3. What is the second ? 


11. If a loaf weighs 6 oz. when flour is $4.50, what ought it to 
weigh when flour is $6 per barrel ? 


12. 112 men can pave a street in 18 days. The work must be 
done, however, in 12 days. How many more men must be employed ? 


13. Ifaloaf of bread cost 5¢ when flour is $6 a barrel, what is 
the probable price when the same loaf can be bought for 4 ¢ ? 


i 


Oral and Written PROPORTION 209 


Notice that the problems given under the subject of proportion 
are not new, but just like those we have solved by other forms of 
analysis. The only new feature is the way of writing the statement 
of the relations and the method of solution depending upon the prin- 
ciple on page 206. This form of solution is used very little in prac- 
tical arithmetic, but is of great value in problems in physics and 
geometry. 


1. If 17 tons of coal are worth $ 135, what are 85 tons worth ? 


SotuTion. 5 x $155 = $675. When one ratio can be easily seen, perform 
that part of the work mentally and thus save time. Use this method when you 
can. 

2. Compare $18 with $198. If I earn the smaller sum in 
54 days, how long ought I to be in earning the larger sum? 


3. The product of the means in a proportion is 17,4. The first 
extreme is 74. What is the missing extreme ? 


4. If 15 sheep cost $ 91, what will 117 sheep cost ? 


5. A clock ticks a times in 14 hours if it ticks 90 times in a 
minute. 


6. If a post 14 ft. high casts a shadow 17 ft. long, how high is 
the church whose shadow is 136 ft. long at the same time ? 


7. Two men are traveling toward each other. A travels 2 as far 
as Bin aday. If A must go 105 miles before they meet, how far 
will B have to go, and what is the distance between them ? 


8. A farmer raised 320 bu. of potatoes on 34 acres of land, and 
the next year he decided to plant 10} acres with potatoes. How 
many bushels do you think he might expect if the yield was a good 
one ? 


9. A grocer paid $ 6.80 for 17 doz. eggs, and found that-he must 
have 84 doz. more to fill his orders. How much did he remit with 
his second order ? 


10. If 6 bbl. of flour are made from 30 bu. of wheat, how many 
barrels should be made from 55 bu. of wheat ? 


210 PROPORTION Written 


1. Compare 371 with 73. If 74 barrels cost $12.50, what will 
374 barrels cost? Explain: 5 x $12.50 = $62.50. 

2. Compare 43 with 46. If 27 mi. of track are laid in 46 da., 
how many miles may be laid in 43 da. ? 


3. One mason can lay 2 as many brick in a day as another. If 
the better man has $3 a a what ought the other to be paid ? 


4. Compare 3 sq. ft. with 2 sq. yd. If napkins containing the 
smaller quantity sell for #3 a dozen, what ought I to pay for a 
dozen tablecloths containing the larger quantity ? 


5. If 36 yards of carpet must be bought for a floor when the 


width of a strip is 36 inches, how many yards are required when 
the strip is 27 inches wide ? 


6. A cog-wheel having 8 cogs plays into another having 24 cogs. 
When the small wheel has made 42 revolutions, how many has the 
larger wheel made ? 


7. If 18 men can do a piece of work in 30 days, in how many 
days can they do it with the assistance of 6 more men ? 
8. A piece of work can be done by 24 men in 30 days. How 
many men will it take to do 4 of the work in 20 days ? 
9. If 9 weeks’ board costs $94.50, what will 12 weeks’ board 
cost ? 
10. If a yacht sails 24 miles in 70 minutes, how long will she be 
in sailing 108 miles ? 
11. If 72 men lay 2 miles of water pipe in 15 days, how many 
days will 48 men require ? 
12. If a train runs 1000 miles in 28 hours, how many miles can 
it run in, 120 hours ? 
13. If 23 yd. of cloth can be bought for $23.10, what should be 
paid for 157 yd. at the same rate ? 


14. If 1 A. yields 22 bu. 3 pk. of corn, how many acres would 
yield 546 bu. ? 


Oral and Written POWERS AND ROOTS 211 


1. Find these powers and roots : — 
10?; 100; 402; 1600; 702; +/4900. 
207; /400; 50?; /2500; 802; 6400. 
30°; V900; 602; 3600; 902; 8100. 
How is a number squared ? 


How are roots related to powers ? 


How many equal factors make a square ? 
What is the square root of 25 x 49 or 1225 ? 
Find the square root of 11,025. 


PROCESS 


oO oOo FPF W WD 


7. Explain the process. | 
8. In the same way find the square root of 9216. 
9. 396,900. 11. 117,649. 
: 10. 194,481. 12. V176,400. 
Therefore 5 x 3 x 7, or 105, is the square root of 11,025. 


Extracting the square root of a number or separating it into two 
equal factors is the reverse of squaring one of these equal factors. 
A careful analysis of the process of squaring will enable us to reverse 
the process and find the square root of a number when it cannot be 
readily found by factoring. 


1. Square 47. Observe that in the process of 


AT Eee cuee multiplication we first find 7 x 7 
AT or 77; next, 7 x 40; next, 40 x 7; 
399 — 724 7 x 40 and finally, 40 x 40 or 40”. 
1880 — 7x 40 + 40? 2. 83? in the same way is equal 


2909 = 7422 «7 x 4042402 » t0 3°-+- 3 x 80-4 80x 3+ 80° =? 

3. Compare 38 x 80 with 80 x 3. Then 3x 804+80x3=2x3 x 80. 
4. 367= 30°4+ 2 x 6 x 3804+ 6’, or 

5. In the same way find 577; 727; 28%. 


212 SQUARING: FIND SQUARE ROOT Oral and Written 


1. Square 64 by the method on the preceding page. 
2. Which of the partial products is the largest? 


WorRK 
G4. . 3. From which digit was it obtained ? 
64 4. Which is the smallest of the partial prod- 
16=42 ucts ? 
480=2 x4 x 60 5. From which digit was it obtained ? 
3600 = 60° 6. If 3600 were taken from the product, most 
4096 =64? 


of what remains is made from what factors ? 
7. Give the squares of all the numbers from 1 to 9 inclusive. 
8. How many figures in each of these squares ? 
9. Square the numbers 10, 20, 30, and so on to 100. 
10. Compare the square of 30 with the square of 3. 
11. Compare 80? with 8’; 60? with 6°; 40? with 4°. 
12. How many figures in the squares of numbers from 10 to 99 
inclusive ? 
13. What is the square of 100? Of 200? Of 999? 
14. How many figures in the squares of numbers from 100 to 999 
inclusive ? 
15. If there are four figures in the square, how many in the root? 
How many in the root when five figures are in the square ? 
16. Give the number of figures in the square root of : — 
9409, 381, 27,225, 182,329, 49,434,961. 
17. How does the number of places in a square compare with the 
number of places in the root ? 
18. Square 0.2; 0.02; 0.4; 0.12; 0.25; 0.03; 0.005. 
19. Compare the number of decimal places in the power with the 
number in the root. 
20. Why can the square of a decimal never contain an odd 
number of decimal places ? 


Oral and Written EXTRACTING SQUARE ROOT 213 


To find the square root, or one of the two equal factors, of 2809. 


Peocwas 1. How many figures in this 
2809 (5043) square ? 
9500—502 2. Then how many in the root ? 
-809=2 x50 x ata? (why ?) 3. Whatisthe square of 50? Of 60? 
300 =2 x 50 x3 4. Between what two squares does 
J=3° 2809 come ? 


5. Then its root lies between what two numbers ? 


6. If the root hes between 50 and 60, the largest of the three 
partial products that make the square is what? 


7. When 2500 is taken from 2809, what two partial products are 
contained in the 509 remaining ? 


8. Most of the 309 is made from which of the partial products ? 


9. Then since 309 is more than 2 x 50 times the number yet to 
find, about what must the number be? 


10. When 2 x 50 x 3 is taken from 309, what one of the three 
partial products remains ? 


11. Is 9 equal to 5?? Then the second number must be 3 and the 
entire root is 50 + 38 or 53. Prove by squaring. 

12. Give the complete process of finding the root of a square 
containing three or four figures. 

In the same way jind the square root of :— 

13. 528. 14.070) 15. 1156. 16. 1764. 17. 2025. 

18. 2916. 19. 3969. 20. 4624. 21. 5625. 22. T0b6. 

23. Prove each by squaring by the method on pp. 211, 212. 

24. Give two factors of 25. Of 25 ft. Of 25 sq.ft. Of $ 25. 


25. In which of these were the factors equal? Of which were 
you able to extract the square root ? 


A concrete number cannot have a square root, that is, two equal 
factors, for one factor must be abstract. Why? 


214 SQUARE ROOT: A SHORTER PROCESS Written 


1. Find the square root of 8836. 


Snort Process We may omit the zeros in the square of 
88'36(94 90, also the zero of the 90. 


81 2. Compare 4 x 18044 x 4 with 4 x 184. 
2 x 90 = 180 | 736 Thus we see that we may also save work 


a ie by sae the 4 to 180 before multiplying 
Solve by both processes and show what you save by the shorter : — 
3. V784. Baan ola. 9. VW5329. 12. 7569. 
4. V3364, 7. V6889. 10. 4489, 13. 2809. 
5. V8464. 8. 2704. 11. 9801. 14. 9409. 


To find the square of 347. To jfind the square root of 


WorK 120409. 
347 Roor 
347 120409 | 300 
90000 =3002 90000 | 40 
120001 5. 200 40 2x 300=600 | 30409 | _ 7 
12000 fice S 24000 =600 x 40 
1600 —40? 64.09 
2100 | 1600=402 
=2X 300 x 7 | 
Ah | -2x340x7 |2x340=680 | 4809 
ZOO EO 0 x ae 4760 =680 x7 
280 | : 
49 =7? 49=7 
120409 1. How did we find the 300 


1. Of the partial products, which |°f the root? What use was 
is the greatest? The next in size? made of it in finding the 40? 
The smallest ? 2. How did we use the 300 

2. Give the five partial products | and the 40 in finding the 7? 
in the square of 265, giving the | © 3. Show by referring to the 
largest first. problem at the left just what 

3. In the same way square 321; | each remainder in this solution 
248 ; 563. contains. 


Written SQUARE ROOT 215 


The process on the preceding page may be used to find the square 
root of any number. 


To find the square root of 2137444. 


PROCESS SHortT PRocEss 
10002 2'18'74'44 | 1000 2'13'T4 '4.4 (1462 
bAd0 7 1000000 | 400 1 
= 113 (444 60 2 1138 


sat 960000 | 2 24 96 
se 1462 = root 28 1774 
177444 286 LG 
60 A 
9860 171600 292 5844. 
2922 5844 
a: Describe the process. 
2922 
Find the square root of : — 
Jeol.) 283024. 6. 6017209. 11. 769129. 
re MS ADE 7. 529984. 12. 935089. 
3. 404496. 8. 484416. 13. 1153476. 
4. 556516. 9. 638401. 14. 1481089. 
5. 755161. 10. 725904. 15. 2540886. 


To find the square root of 0.501. 


PRocESS ExpLanation. As the square of tenths gives 
0.501 (0.707 + hundredths, to get the first root figure we take 
the first two figures at the right of the point or 


aes 
UO Se Meay .50, the root of which is nearly 0.7. Each new 
1.4 | 0.0110 quotient figure is determined by division, as in 
007 0.009849 the case of integers. Since the square of a deci- 
1.407 0.001151 mal cannot give an odd number of figures, this 


decimal must be an imperfect power, and the root 
cannot be exactly determined. This is indicated by a + or — after the last 
root figure. 


EXERCISES IN 


Find the square root of:— 


16010, 0625. 5. 0.89. 

2. 0.9216 6. 19.467. 

3. 42.225 7. $24.9. 

4. 0.783 ref BUG U es 

A. V320=V$4=8 

Bet en 0.875 06127 

CO. Vit=vV58 = $= 23 

TD) ‘Li —/40 i 6.38245+ 

BE. V63 =V6.375 = 2.524 

HHI 

IV 

17. V44t 19. 61% 

1s. V5 20ee De 

Extract the square root of :— 
_ Oral 

1. 14400. LTA9: 

2. 48 12;.° 0.049; 

3. (54)? 13. 0.00490. 

4. (163) 14. 625. 

5. 0.09. 15. 0.625. 

6. 36 x 49. 16. 16 million. 

whe Ag 8 Si: LT tes 

8. (874)’. 18. 304. 

Goo x Sie LO. cies 

10. 0.0625. 20. 107. 


SQUARE ROOT Written 
9. 0.64. 18. 225.9009. 
10. 0.064. 14. 2044900. 
11. 1952-4: 15. 76.3876. 
12. 783.95. T638U.0; 

In finding the root of 
fractions : — 


I. First change them to 
simplest form, asin A or C. 

II. Use the method in A 
or C when both terms are 
perfect powers. 


Use B or E when both terms are imperfect powers. 


. D may be used when the denominator is a square. 


21. ~/825. 83.) Ledae 
Py ey PETOES 24.1 eee 
Written 

1. 94249. 11. 95,;. 

Ay OAs 12,16" 

ite lhe iw 

4. 1008016. 14. 4. 

Bi) 9834496. | 15. 2. 

6. 62742241. 16. 1274. | 

7. 2033.1081. 17. 785. 

Sp ts 18. 3444736. 

9. $4+2+46 19. 177+ 257 
10. 998001. 20. 0.741. 


Oral and Written SQUARE ROOT: THE FORMULA 217 


1. The law governing the three partial products forming a square 
may be more easily remembered if stated in a formula as follows: — 


(a+ bP? =a?+2ab+b’. 
Thus, 23° = (20 + 3) = 20° + 2 x3 x 204 32= 400 +1204 9= 529. 


2. 16 = (124 4)?= 144+ 96 + 16 = 256; thus we see that a and b 
need not represent fens and ones respectively, but any two numbers. 


3. Knowing that 25° = 625, find 27°, as in Example 2. 


Square Root 


° PROCESS 
a b 
a+ 2ab+b?=7056. (804 4 
a? = 6400 
2ab+0° or (2446) b= 
Z2a=160 


b= 4 
(2a+b) =164 656 =2 ab +0? 


EXPLANATION. 7056 comes between the square 6400 and 8100, hence its root 
is between 80 and 90. Then a must be 80, and a?, 6400. ‘Taking this out, what 
remains ? 

The remainder, 656, then is made up of two factors, 2a@+6,and 6. 2aofone 
being known is used as a trial divisor to get a clew to the other factor, 6, which 
in this cannot be more than 4. The whole factor, or the complete divisor, then is 
160 + 4, or 164. Since this with 4 makes 656, the exact root is 84. ; 

If there had been a remainder, we should have next considered all the root 
found, or 84, as a and used 2 a, or 168, for our next trial divisor to find the next 
root figure. 


Using the formula, find to two decimal places the square root of : — 


1. 80. 6, 17.45.> 11 3.00. 16:0 027) 
2. 10.35. Toe 12. 0.7854. ab oats? oi 
3. 6.43. 8. 8.56. 13. 391. 18. 348. 
4. 9.8. 9. 9.42. 14. 74. 19. 64.01 
Bact. 10. 0.7. 15. 0.360. 20. 36 


rs] 
, 


918 APPLICATIONS OF SQUARE ROOT Oral 


1. Draw a right triangle with the sides which form the right 
angle, 3 inches and 4 inches respectively. 


2. Measure the length of the other side, or hypotenuse. 
3. Draw a square on each of the three sides as base. 


4. Compare the square on the hypotenuse with the sum of the 
squares on the other sides. 


Pythagoras proved about 500 s.c. that the fact that we find true 
here is true for any right triangle, viz. that 


The square on the hypotenuse is equal to the sum of the squares on 
the other two sides. 


5. Carpenters make use of this fact, in laying out the foundation. 
for a building, when they want to form a right angle. A line 8 feet 
long is taken in one direction along which the foundation is to be 
made. Another line 6 feet long is fastened to one extremity of the 
first line and moved until a 10-foot rod will just reach the outer 
extremity of the two lines. Draw such a figure, and show that this 
gives a right triangle. 


6. Use the test in 5, and find whether the walls of your school- 
room are perpendicular to the floor. 


7. If the square on the hypotenuse is 100 sq. in. and on one of 
the sides 36 sq. in., what is the length of each side of the triangle ? 


Denoting the hypotenuse by H, the base by B, and the perpendicu- 
lar by P, when these are abstract numbers representing the number 
of units in the dimensions, we may state from the above principle 
the following formule : — 


H=VJVB? +P? 8. Explain the formule. 
B=V ER? ~ P? 9. 1f Hf asloeand) Pe peer 
P=VH?— B 10.) iB bands P= Ome eae 


11)\ If = 25/ and B= 20a 


Written APPLICATIONS OF SQUARE ROOT 219 


The Right Triangle 
The truth of the Pythagorean theorem, stated on the preceding 
page, may be seen by drawing, or cutting from cardboard, figures 
like the following : — 


Let ABC be the right triangle. The square on the PRUNE 
AC is equal to the 4 triangles, 1, 2,3, and 4, and the small square, 5 
Now put 1 and 2 in the position of the figure at the right, and ihe 
figure is equal to a square on AB and one on CB’. 


1. The base of a right triangle is 48 feet and the perpendicular 
is 36 feet. What is the hypotenuse ? 


2. The hypotenuse is 85 feet and the perpendicular is 51 feet. 
What is the base ? 


38. The base is 76 feet and the hypotenuse is 95 feet. What is 
‘the perpendicular ? 

4. What is the diagonal of a rectangle 92 ft. long and 69 ft. wide ? 

5. What is the diagonal of a 30-ft. square ? 


6. What is the longest line that can be drawn on a sheet of 
paper 16 inches wide and 20 inches long? 

7. What is the diameter of the largest wheel that can be got 
through a doorway measuring 7 feet by 5? 


8. What is the distance between the opposite corners of a field 
200 rods long and half as wide ? 


220 APPLICATIONS OF SQUARE ROOT Written 


ISOSCELES TRIANGLE EQUILATERAL TRIANGLE 


Prove by cutting or measuring that — 


(1) The altitude of an isosceles triangle bisects the base. 


(2) The perpendicular from any vertex of an Bar Re triangle to 
the opposite side bisects it. 


Since an equilateral triangle is also isosceles whatever side is 
taken as base, (2) could have been inferred from (1). 


1. If the base of an isosceles triangle is 12 and the equal sides 10, 
what is the altitude ? 


2. Find the altitude of a triangle whose sides are each 10 inches. 


3. A rectangle measures 22 ft. by 10 ft. How long is its diagonal ? 


4. The foot of a 25-foot ladder is 12 ft. from the side of the house 
against which it leans. How far from the ground is its top? 


5. What is the area of a right triangle whose longest side is 20 ft. 
and its shortest 8 ft. ? 


6. Find the altitude of an equilateral triangle 
whose side measures 24 ft. Find the area. 


7. What will it cost to fence a square field 
containing 5 A. at $1.25 a rod? 


8. A regular hexagon is made up of six equi- 
lateral triangles. Study the figure and discover 
how to inscribe one in a circle. 


A REGULAR HEXAGON 


9. Find the area of a regular hexagon whose sides are each 10 
inches. 


Written APPLICATIONS OF SQUARE ROOT ZA 


Remember that we cannot take the square root of a concrete num- 
ber, such as 25 sq. ft., but of 25. In all the formule that follow, we 
are to consider areas, lengths, etc., as the nwmber of units, and hence 
deal with abstract numbers. 


1. Since the area of a circle = 77”, or 3.1416 x the square of the 


radius, eran What is the radius of a circle whose area is 
T 
78.54 sq. in. ? 
2. What is the diagonal of a floor 25 feet long and 16 feet wide ? 


3. The diagonal of a rectangle 30 feet long measures 42 feet. 
What is the width of the rectangle ? 


4. The perimeter of a rectangle is 36 feet. Its width is half its 
length. What is its diagonal ? 


5. What is the diagonal of a square containing 32 square inches ? 


6. The top of a 30-foot ladder, which is placed 16 feet from the 
side of a house, reaches a window sill in the third story. How far 
from the ground to the window sill ? 


7. Two yachts start together. One sails due north and the other 
due east, each at the rate of 12 miles an hour. How far apart are 
they at the end of 4 hours ? 


% 


8. What is the area of a circle drawn with an 18-inch radius ? 
9. The area of a circle is 24.3474 sq. in. What is its diameter ? 


10. A line reaching from the bank of a stream to the top of a 
50-foot pole on the other side is 275 feet long. What is the width 


of the stream ? , 


11. The base of an isosceles triangle is 20 feet and its altitude 
15 feet. What is the length of one of the equal sides ? 


12. A gable-roof house is 24 feet wide. The distance from the 
plate to the ridgepole is 12 feet. ‘The rafters project 1 foot over 
the eaves. How long are they ? 


222 APPLICATIONS OF SQUARE ROOT Written 


1. What is the length of a square equal in area to a rectangle 
24 rd. long and 33 ft. wide? 


2. What is the longest straight line that can be drawn on the 
ceiling of your schoolroom if it measures 32 ft. by 30 ft. ? 


3. Compare the perimeter of a rectangle 48 in. by 12 in. with 
that of a square of equal area. 


4. How much do I save by crossing along the diagonal of a square 
that contains 1296 sq. rd. instead of going around its two sides ? 


5. How long is an acre of land in the form of a square ? 


6. How long a guy will support a derrick 48 ft. high if fastened 
85 ft. from its base ? 


7. The hypotenuse of a right triangle measures 90 ft. The 
other sides are equal.- How long are they ? 


8. Two poles are 100 ft. apart. One is 60 ft. high, and the other 
80 ft. How long a line will connect their tops ? 


9. A rectangle 3 times as long as wide contains 3888 sq. ft. 
What are the dimensions? (Hint. Divide it into 3 squares.) 


10. What is the altitude of an equilateral triangle whose base is 
24 feetr? 


.11. The base of an isosceles triangle is 84 feet, and one of the 
other sides is 50 feet. What is the altitude ? 


12. From the corner of a 12-inch square I cut an isosceles triangle 
one of whose sides is 4 inches. What is the area of that part of the 
large square which remains ? 


13. My son’s kite is 1500 feet directly above the spot on which 
I am standing, and my son holds the string 1800 feet away. How 
much string has he let out? Allow 25 ft. for sagging. 


14. How many rods do I save by taking the diagonal of a field 
75 rods wide and 200 rods long, instead of going around the corner ? 


Oral PRISMS AND PYRAMIDS Hadas) 


C 


SC | ey a 
D 
A 
RECTANGULAR TRIANGULAR RECTANGULAR TRIANGULAR 


PRISM PRISM PYRAMID PYRAMID 


A Pyramid is a solid whose base is a polygon and whose sides or 
faces are triangles meeting at a common point called the vertex of 
the pyramid. 


If the base is a regular polygon, as a square, or ‘an equilateral 
triangle, and the sides are equal isosceles triangles, the pyramid is a 
regular pyramid. 

The distance from the vertex to any side of the base of a regular 
pyramid is the slant height. 


1. The distance from the vertex to 
the side is the altitude of the triangle, 
hence it divides the side into two equal 
parts. Why ? 

2. Construct from cardboard a pyra- 
mid whose base is a 4-inch square, and 
whose edges AC, etc., are 6 inches. 

Draw a model, and leave lapels for 
pasting. 


Written 

3. What is the length CD, or the slant height of this pyramid ? 

4. Having found CD, and knowing OD, observe the figure at the 
top of the page, and find the height. (Observe that the altitude of 
a regular pyramid meets the base at its center.) 

5. How could you have found AO and then the height from OA 
and AC’? Find it. 


994 PRISMS AND PYRAMIDS Oral 


1. Make a prism having exactly the same base and altitude as 
the pyramid you have made. Test the accuracy of your construction 
by measuring, as in the figure. 


Make an opening in the base of the pyramid, and fill with dry 
sand, and fill the prism from this as a measure. 


2. What do you find true of their volumes ? 


3. Make other prisms and pyramids as your teacher may direct, 
and test the accuracy of the following : — 


The volume of a pyramid is 4 of that of a prism having an equal 
base and an equal altitude. 


4. A square pyramid is 12 ft. high and measures 3 ft. along one 
side of its base. What is its volume ? 


5. What part of a square prism is whittled away by a boy who is 
making the largest pyramid possible out of it ? 


6. The volume of a square prism is 86 cubic inches. What is the 
volume of a square pyramid of the same base and altitude ? 


7. The area of the base of a triangular prism is 4 square feet. 
Its altitude is 5 feet. What is its volume ? 


8. The contents of a square prism are 28 cubic feet. Its base 
covers 4 square feet. What is its altitude ? 


9. The contents of an hexagonal prism are 42 cubic inches. The 
altitude is 6 inches. What is the area of the base ? 


Oral and Written PRISMS AND PYRAMIDS 995 


1. A granite shaft 10 ft. high and 20 in. square is surmounted 
by a square pyramid 2 ft. in altitude. The contents of both ? 


2. Which is more easily measured, the slant height or the alti- 
tude of a pyramid? Which line of a triangle is the slant height of 
a regular pyramid ? 


3. The slant height of a square pyramid is 15 inches, and the 
side of the base 10 inches. [ind its contents. 


4. The area of the base of a pentagonal prism is 624 sq. in.; its 
altitude is 24 in.; the contents ? 


5. A square prism has a base 2 feet long and an altitude of 10 feet. 
It is made of granite weighing 165 pounds to the cubic foot. What 
is the weight of the prism ? 


6. How many surfaces has a square prism? What is the shape 
of each one? 

7. A hexagonal pyramid is one having a hexagon as base. How 
many triangles make its visible surface? Of what kind? 

8. What two lines in an isosceles triangle must be known in order 
to find its area? 


9. What is meant by the slant height of a regular pyramid ? 


The total area of all the faces of a prism is called its convex 
surface. 


10. A square pyramid has a slant height of 12 inches and a base 
of 4 inches. What is its convex surface ? 


11. An octagonal pyramid’s slant is 16 inches, and the perimeter 
of its base is 48 inches. What is its convex surface ? 


12. All four sides of a pyramid are equilateral triangles 6 inches 
long. Find the slant height and the convex surface. 


13. The altitude of a square pyramid is 15 in. and the side of its 
base is 12 in. Required its contents. 


14. Find its slant height and convex surface. 


226 CYLINDERS AND CONES Oral 


A solid having a circle for a base and tapering uniformly to a 
vertex is a cone. AC is the slant height. While there are other 
kinds of cones, we shall consider the kind described above. In this 
kind the altitude from the vertex passes through the center of the 
base. ) 


1. How can you find the altitude when the slant height is known? 


2. Make a cone whose base is a circle, whose radius is 2 inches, 
and whose slant height is 6 inches. 
Make a model as in the margin. 

8. How long is the arc CB? 
What is its radius ? 

4. What will be the height of 
the cone ? 

5. Make a model for a cyl- 
inder of the same dimensions. 

6. What will be the size and 
shape of the convex surface ? 


7. Test the accuracy of your 
construction by measuring as shown in the figure at the top of the page. 


8. Using the cone as a measure, fill the cylinder with dry sand. 
9. How do their volumes compare ? 
10. Make other sizes and show that — 
The volume of a cone is equal to 4 of that of a cylinder having an 
equal base and the same height. 


11. How do we find the volume of a cylinder ? 


Oral and Written CYLINDERS AND CONES 227 


1. If a cylinder weighs 3 pounds, what will be the weight of a 
cone of the same material having the same base and altitude ? 


2. The largest possible cone is turned in a lathe out of a cylinder 
6 inches long and 3 inches in diameter. What part of the cylinder 
goes into shavings? How many cubic inches in the cone ? 


3. The base of a cone is 6 square inches and its altitude is 
12 inches. Find its contents. 


4. The contents of a cone are 24 cubic inches. The altitude is 
12 inches. What is the area of the base ? 


5. The diameter of the base of a cone is 4 feet. Its altitude is 
9 feet. What are its contents ? 


6. A cylinder of ebony weighs 1 lb. 8 0z. What will an ebony 
cone of the same base and altitude weigh ? 


7. What is meant by a sector? How many lines in its boundary ? 


8. Show that the are of a sector multiphed by 4 of the radius 
will give the area of the sector. Compare the method with that of 
finding the area of a circle. 


9. The convex surface of a cone is a sector, the circumference of 
the base being the are of the sector, and the slant height of the cone 
its radius. The circumference of the base is 8 inches, and its slant 
height 10 inches. Area of its convex surface ? 


10. What is the convex surface of a cone whose altitude is 4 feet, 
and the diameter of whose base is 3 feet ? 


11. The radius of the base of a cone is 34 feet. The slant height 
is 5 feet. Find the entire area. (The area of the base + area of the 
convex surface. ) 


12. What is the convex surface of a cylinder 7 feet in diameter 
and 10 feet high ? 


13. How many yards of cloth will be required to make a conical 
tent 12 feet in diameter and 15 feet high? Add 5% for seams. 


228 


SURFACE OF SPHERES 


Oral 


1. Cut away any slice of a sphere, as an apple. What is the 


form thus exposed ? 

2. When a sphere is bisected, that is, 
divided into two hemispheres, the plane sur- 
faces thus exposed are great circles of the 
sphere. Would the diameter and circumfer- 
ence of one of these circles be the diameter 
and circumference of the sphere ? 

3. Wind the surface of a hemisphere as 
in figure C with a hard, waxed cord. (Place 
a small tack in the center, and around this 
wind the cord.) 

4. With the same cord wind a great circle 
as in figure D. 

5. Compare the two lengths, and thus the 
two surfaces. 

6. Using cords of different sizes, and if con- 
venient several sizes of spheres, show that — 

The surface of a hemisphere is twice that of 
a great circle. 

7. Compare the surface of a sphere with 
that of a great circle. 

8. What is the area of a great circle of a 
sphere whose radius is 4 inches? What then 
is the surface of the sphere ? 

Remember then that — 

The surface of a sphere =47m or 7d’. 
(ry = radius; d = diameter.) 

9. Show that 4 7? = qd? 

10. What is the surface of a sphere whose 
diameter is 10 inches ? 


‘ 


f 
J 


el 


if 


i 


« 


| 


YZ 
oy) 


‘ 


11. When the radius is 4 inches, what is the surface of a sphere ? 


Oral VOLUME OF SPHERES 229 


1. Ifa sphere should be dissected as in the accompanying illustra- 
tion, what solids would its parts most resemble ? | 


2. What line in the sphere forms the altitude of each pyramid- 
like solid ? 

3. What forms the base of each ? 

4. Taken together, what will the bases of all the pyramid-like 
solids make ? : 

5. If these were perfect pyramids, how would the volume of any 
one be found ? ‘ . 


While these solids are not pyramids, for their bases are not plane 
figures, yet it is proven in geometry that — 

The volume of a sphere is the same as that of a pyramid whose base 
is the surface of the sphere and whose height is the radius of the sphere. 


6. What should we obtain by multiplying the surface of a 
sphere by 4 of its radius ? 

7. The surface of a sphere is 113 sq. in., and its radius 3 in. 
What are its contents ? 

8. How is the surface of a sphere found? 4 of the radius is what 
part of the diameter ? 


9. Read and explain the following : — 
2x 4 REX 314164 BP x 3.1116, or 4 x R'= volume of a sphere; or 


2 pat Dae a eA i x 3.1416, or a = volume of a sphere. 


230 SURFACE AND VOLUMES OF SPHERES Written 


1. What part of a 2-inch cube is a 2-inch sphere ? 


2. If a sphere 3 inches in diameter is carefully turned out of a 
3-inch cube, what part of the cube will go into shavings, and what | 
part will remain in the sphere ? | 


3. If asphere is 0.5236 of a cube of the same diameter, what will 
be the contents of a sphere 4 inches in diameter ? Compare 0.5236 


Withce 
6 


4. If a cubic foot of iron weighs 450 pounds, what is the weight 
of an iron sphere 12 inches in diameter ? 


5. A cubic foot of ivory weighs 114 pounds. What is the weight 
of a set of 4 billiard balls 2 inches in diameter ? 


6. How many cubic miles in the moon if we call its diameter 
2000 miles ? 


7. If we call the diameter of the earth exactly 8000 miles, how 
many moons will be equal in volume to the earth? Shorten your 
work by cancellation. 


8. Two 4-inch spheres are dropped into a pail even full of water 
and holding 864 cubic inches. How many cubic inches of water are 
displaced ? 


9. Find the square inches in the surface of a 6-inch sphere. 


10. How many square miles in the surface of the moon? Call its 
diameter 2000 miles. 


11. A cubic foot of water weighs 1000 ounces, and gold is about 
19 times as heavy. What will a sphere of gold 3 inches in diameter 
weigh ? ) . 

12. If it costs $3 to gild a 3-inch ball, what will it cost to gild a 
4-inch ball? Shorten your work by cancellation. 


13. If a ball 2 inches in diameter weighs 18 oz., what will a ball 
of the same material, and 6 inches in diameter, weigh ? 


Oral MENSURATION: SIMILAR FIGURES VoL 


1. What is the ratio of a 2-inch square to a 4-inch square ? 
2. What is the ratio of a 2-inch square to a 5-inch square ? 


3. What is the ratio of a 2-inch circle to a 4-inch circle? What 
common factors enter into the areas of any two given circles ? 


4. Compare a 3-inch circle with a 5-inch circle. 


5. Explain the statement : — 


A 3-inch circle: a 5-inch circle = (3)? x 3.1416: (8)? x 3.1416, or a 
3-inch circle: a 5-inch circle = 37: 5”. 


6. Ifa rectangle is 2 by 3, what will be the length of another of 
the same form or shape that is 4 wide? 6 wide? 12 wide? 


7. Two rectangles whose corresponding sides have the same 
ratio are similar. All surfaces of the same form or shape are 
similar surfaces. Are all squares similar? All circles? All equi- 
lateral triangles ? 


8. Compare a rectangle 2 by 3 with one 4 by 6. ~ 
9. Compare a rectangle 3 by 6 with one 5 by 10. 
10. Are the rectangles in Exs. 8 and 9 similar? Why ? 


11. Observe that in the squares, circles, and rectangles that you 
have tried, their areas have the same ratio as the squares of their 
corresponding lines. Try other figures that you know to be similar, 
and see whether this is true : — 


Similar surfaces have the same ratio as the squares of the ratios of 
their corresponding lines. 


12. Compare two equilateral triangles whose sides are respec- 
tively 5 inches and 5 inches. 


13. Are the surfaces of all spheres similar surfaces? If it costs 
50 ¢ to gild a 3-inch sphere, what will it cost to gild a 9-inch sphere? 


14. Ifa lot 60 ft. square costs $300, what will one 120 ft. square 
cost at the same rate ? 


* 


Lay MEASUREMENTS: SIMILAR SOLIDS Oral 


1. What is the volume of a 2-inch cube? Of a 4-inch cube? 

2. Compare a 2-inch cube with a 4-inch cube. What is the 
ratio of 2 to 4? 

3. What is the volume of a 4-inch sphere? Explain: ¢ x 2° 
x 3.1416. 

4. What two factors are common to the volume of any two 
spheres ? 

5. Compare a 3-inch with a 5-inch sphere. Explain : — 

4x (8)8 x 3.1416: 4 x @)® x 3.1416 = 3°: 5° = Ae. 

6. What is the ratio of the diameters in Ex.5? What was the 
ratio of their volumes ? | 

7. Compare a 38-inch cube with a 5-inch cube as to their edges 
and volumes. 

8. Solids that have the same shape are similar solids. Name 
some similar solids. 

9. In the preceding problems, what did you notice to be the 
relation of volumes of similar solids to their like lines ? 


10. Take other solids that you know to be similar, and see whether 
you find this to be true : — 


Similar solids have the same ratio as the cubes of the ratios of their 
corresponding lines. 

11. The ratio of a 4-inch cube to a 12-inch cube is (4)’, or a. 

12. What is the ratio of a 4-inch sphere to a 12-inch sphere ? 

13. Of a 6Linch cube to a 124-inch cube ? 

14. Of a 61-inch sphere to a 123-inch sphere? 

15. Of a 162-inch sphere to a 331-inch sphere ? 

16. Ifa 23-inch sphere weighs 3 lb., what will a 5-inch one of 
the same material weigh ? 

17. How many 14-inch cubes can you put into a box 6 inches 
each way ? 

18. How many }-inch balls can be molded from a 6-inch ball ? 


Oral and Written MEASUREMENTS 250 


Similar Surfaces and Volumes 


1. The ratio of the flow of water through two pipes depends 
upon the area of the cross section of the two pipes. Compare the 
flow through a 4-inch nozzle and a 2-inch nozzle. 


2. If two triangles are similar, their corresponding sides and 
altitudes all have the same ratio. If the ratio of the altitude of 
two triangles is as 3 to 9, or 4, what is the ratio of their areas? 


3. If a square lot 60 ft. long costs $300, what will one of the 
same shape 3 times as long cost ? 


4, Compare the strength of a rope 2 in. round with that of one 
3 in. round. ; 


5. If it costs $8.25 to gild a sphere 20 inches in circumference, 
what will it cost to gild one 30 inches ? 


6. A %-inch faucet fills a tank in 20 minutes; a 4-in. faucet 
will fill it in @ min. 


7. The ratio of two similar triangles is 25; the ratio of their 
altitudes is a. 


8. To paint a conical steeple 30 ft. high costs $35; to paint a 
similar one 45 ft. high costs, at the same rate, $2. 


9. A conical tent 16 ft. slant height costs $13.50; one of the 
same shape measuring 4 ft. more would cost $a. 


10. If a 2-inch sphere weighs 1 lb., how much will a 6-inch 
sphere weigh ? 
11. If a rectangular bin 5 ft. long contains 75 bu. of oats, how 


many bushels will a similar bin 124 ft. long contain ? 


12. Itrequires 90 min. to fill a cylindrical tank 3+ ft. in diameter. 
At the same rate, how many minutes will be required to fill a simi- 
lar tank 14 ft. in diameter ? 


234 SIMILAR TRIANGLES Oral 


1. Describe similar surfaces. 
2. Make two similar triangles. Are their corresponding angles 
equal ? 


3. Draw atriangle, ABC, as in the figure. C 
Draw EF parallel to AB. By the use of a 
protractor compare the angles FHC and 
BAC. Also angles CFE and CBA. E F 
4. Are triangles ABC and EFC simular; 
that is, do they have the same shape ? 
5. Make a triangle in which AC is 6 inches and CB 3. Mark off 
CE equal to 4 inches and CF 2 inches. Are the two triangles 
similar ? 


6. What is the ratio of CA to CH? Of CB to CF? 


7. Cut similar triangles from cardboard. Measure their sides 
and discover that — 


B 


In similar triangles the ratios of the corresponding sides are equal, 
and the ratio of any two sides of one is equal to the ratio of the corre- 
sponding sides of the other. 


. 8. Inaccessible distances may be found 
by the principle of similar triangles. Sup- 
pose we are to find the distance AB across 
a small lake. By measuring from A to C, 
and from B through O to D, making the 
ratio of OC to OA the same as of OD to 
OB, we have similar triangles. 

If OC =10A, and CD measures 20 
rods, what is AB? 

Note. Make OC any convenient part of OA and then OD the same part of 
OB. In the figure OC = 3 OA, and OD=3 OB. 


9. When a vertical rod 6 feet high casts a shadow 9 feet long, a 
tree casts a shadow 150 feet long. How high is the tree? 


Oral SIMILAR TRIANGLES 235 


1. A boy, wishing to find the 
height of a pole CH, made a piece 
of apparatus which he called his 
“surveying instrument.” It con- 
sisted of a right triangle whose 
two legs were equal. It stood 3 
feet from the ground. He moved 
it along until the point C could 
just be seen along the hypotenuse 
of the triangle when the base of : = 
the triangle AF was parallel with = = : = 
the ground. A line with a weight 
(a plumb line) hung from A. If DE was 27 feet, how high was the 
pole? (Triangles A4F'H and ABC are similar. Why ?) 


2. If HF had been twice AF, and DE had been 40 feet, what 
would CE have been ? 


3. Make such an instrument, and find the height of trees, tele- 
graph poles, ete. 


4. Make one with the triangle having one leg twice the other, and 
measure the same heights. Do your results check ? 


5. Two triangles are similar. One has sides 4, 5, and 7 inches 
respectively. The long side of the other is 21 inches. What are 
the other sides? What if the short side of the latter were 2 inches ? 


6. I wish to find the distance AB. AC is 
15 rods and OC is 5. I measure from B 
through O to D. If BO is 8 rods, what shall 
Imake OD? Why? 

I measure DC, and find it to be 74 rods. 
How far from A to B? 


7. In this way measure distances on your 
school lot. 


236 LAND MEASURE: TOWNSHIP AND SECTION Written 


1. Government lands are divided by parallels and meridians into 
townships six miles square, containing 36 sections or square miles. 
Each section is divided into half sections and quarter sections. How 
many acres in a section? In a quarter section ? 

2. A township is designated by its number north or south of a 
base line running east and west, and east or west of a principal meridian 
running north and south. 

Thus, Cis Township 4 N., Range 3 H. WhatisA? Whatis B? 

3. The 36 sections into which a township is divided are numbered 
as in the accompanying figure. Point out section 15. 

4. Half and quarter sections are designated as W. or N. half 
sections, etc.; and §8.W. or N.E. quarter sections, etc. How many 
acres in 8. $ 8.W. 4 Sec. 15? 


Township. Section 15. 


Surveyors generally use, in measuring land, a steel chain 100 ft. 
long, divided into foot links, or a steel tape line of the same length 
graduated to feet and tenths. Sometimes a Gunter’s Chain is used. 
It contains 100 links, each 7.92 in. long. The chain is 4 rods, or 
66 ft., or 792 in. in length. 80 chains, or 320 rods, measure a mile. 


5. How many square rods in a square chain ? 
6. How many square chains make 160 sq. rds, or 1 acre? 


7. How many acres in 8.W. 4 N.E.4 Sec. 27? Draw diagram 
and locate it. 


Written MENSURATION: REVIEW Yai 


1. Find the cost of plastering the walls and ceiling of a room 
18 ft. long, 15 ft. wide, and 9 ft. high, allowing 4 of the area for 
openings and wood-covered portions. Price 124¢ per square yard. 


2. Find the area of a right triangle, base 25 ft., hypotenuse 
60 ft. 


3. A rhomboidal field contains 5 acres, and measures 50 rods 
along a straight road. How wide is it? 


4. Name the six quadrilaterals and the four parallelograms. 
Draw a trapezoid and its equivalent rhomboid and rectangle. 


5. Required the area of the entire surface of a stick of timber 
18 ft. long, 4 in. thick, 8 in. wide at one end, 12 in. at the other. 


6. The diagonal of a trapezium is 221 ft., and the perpendiculars 
lrawn from the vertices of the angles opposite it are 16 ft. and 12 ft. 
respectively. What is the area of the trapezium? Draw it. 


7. Find the cost of 28 “six-by-four” joists, averaging 18 ft. in 
length at $32 per M. . 


8. What is the area of a walk 3 ft. wide, around a semicircular 
flower bed, the straight edge of which measures 12 ft. ? 


9. There is a difference of 6 in. in the diameter of the wheels of 
a carriage. The fore wheel turns 1000 times in going a certain dis- 
tance. The hind wheel turns 2 times, and is 4 ft. in diameter. 


10. What is the axis of a sphere 4 ft. in circumference ? 


11. From a sheet of zinc, weighing 16 lb., and measuring 8 ft. by 
4 ft., a square was cut, reducing its weight to 114 lb. How long was 
the square ? 


12. How much ground is covered by 12 cords of 4-ft. wood piled 
2 ft. high ? 


13. A granite sphere barely clears a gateway 2 feet wide. Find 
its contents. 


238 MENSURATION: REVIEW Written 


1. A span of horses draws a load of brick weighing two tons. 
The brick are of the ordinary size, 8 x 4 x 2, and weigh 100 lb. to 
the cubic foot. How many bricks in the load ? 


2. Find the contents of a cone 6 in. in altitude and 2 in. in 
diameter at the base. 


3. Find the slant height of a square pyramid 12 in. in altitude, 
base 8 in. on a side. 


4. Find the entire area of a hemisphere 15 m. in diameter. . 


5. How long is the equator, the equatorial semidiameter of the 
earth being 3963.296 miles ? 


6. Compare the perimeters of a rectangular field 60 rd. by 30 rd., 
of an equivalent square field, and of a circular field of the same area. 


7. The inside dimensions of a cellar are 16 ft., 12 ft., and 8 ft. 
The wall is to be two feet thick. How many cubic yards of earth 
will need to be removed ? 


8. A cylindrical 8-in. driven well is 76 ft. deep. How many 
cubic feet of earth, etc., have been taken out ? 


9. One fire-engine throws a 2-inch stream, another a 13-inch 
stream. Compare the quantities of water thrown. 


10. One piece of shafting 2 in. in diameter weighs 300 lb. What 
is the weight of a similar piece 31 in. in diameter ? 


11. How deep shall a 12-foot square bin be made to hold 1728 
bushels ? 


12. How many cords of wood in a section of a giant pine 18 ft. 
long and 16 ft. in diameter ? 


13. Ifa 2-in. rope breaks with a weight of 8000 lb., what weight 
might break a similar 3 in. rope ? 


14. Give area of basin required for a fountain that throws its 
spray out 15 feet. 


THE METRIC SYSTEM OF WEIGHTS AND MEASURES) 239 


The English system of weights and measures, the system in com- 
mon use in the United States, lacks a uniform scale of relation. 
HMOiexa tiles 20 loiter os tbe = liyd. 3 0. yO. = 1 Td.,etc,.and 
2 pt. =1 qt.; 4 qt.=1 gal. The United States system of money 
has a uniform decimal scale, and thus any part of a dollar can be ex- 
pressed as a decimal fraction. Thus 3 dollars, 5 dimes, and 7 cents 
can be expressed $3.57. 


The metric system grew out of an attempt by the French govern- 
ment to supply a system of weights and measures that would have a 
uniform decimal scale of relation that would thus facilitate computa- 
tion by enabling one to change a unit to any other unit by simply 
moving the decimal point. 


The committee appointed to report upon a standard unit thought to 
make this unit, which was to be the unit of length, some part of some 
well-defined portion of the earth’s circumference. <A careful compu- 
tation of the length of earth’s quadrant through Paris was made, and 
0.0000001 of this distance was taken and called the meter. The 
meter is about 39.57 inches in length. 


Nore. While a slight error was made in fixing the standard unit, this does 
not affect the usefulness of the system. 


From the meter, all units of length, surface, volume, capacity, and 
weight are derived. 

The unit of weight is the weight of a cube of water 0.01 of a meter 
en anedge. This is the gram. 

The unit of capacity is a cubical vessel 0.1 of a meter on an edge. 
This is a liter (1é'ter). 


Nort. The Metric system is in general use by nearly all civilized nations 
except Great Britain and the United States. It is used by some departments of 
the United States government, and in the sciences. It was legalized in France 
in the early part of the nineteenth century. 


The Metric system is a decimal system, ten units of one denomina- 
tion making one unit of the next higher. 


240 


THE METRIC SYSTEM Tables 


Decimal parts of the standard or principal unit are denoted by 
Latin prefixes; multiples of the same, by Greek prefixes. 


From THE LATIN From THE GREEK 
Milli means 0.001 Myria means 10,000 
Centi means 0.01 Kilo means 1000 
Deci means 0.1 Hekto means 100 


Deka means 10 


In the tables units in common use are in bold-faced type. 
There is no uniformity as to the abbreviations used. The ones 


given h 


ere are in general use. 


UNITS OF LENGTH 
Standard unit, the Meter - 


TABLE : IQUIVALENTS 
10 millimeters (mm.) = 1 centimeter (cm.) = 0,8937079 inch 
10 centimeters = 1 decimeter (dm.) 
10 decimeters = 1 meter (m.) = 39.87079 inches 
10 meters = 1 dekameter (Dm.) 
10 dekameters = 1 hektometer (Hm.) 
10 hektometers = 1 kilometer (Km.) = | Beat ARR 


| 0.621382 miles 
10 kilometers = 1 myriameter (Mm.) 


UNITS OF SURFACE 
Principal unit, the Square Meter 


As the units of surfaces are squares whose dimensions are the 
corresponding linear units, it takes 10? or 100 units of one denomi- 
nation to make one of the next. 


TABLE EQUIVALENTS 
100 sq. millimeters (sq. mm.) =1 sq. centimeter (sq.cm.) =0.155 sq. in. 
100 sq. centimeters =1 sq. decimeter (sq. dm.) 
100 sq. decimeters =1 sq. meter (sq. m.) = 10.764 sq. ft. 
100 sq. meters =1 sq. dekameter (sq. Dm.) 
100 sq dekameters =1 sq. hektometer (sq. Hm.) 
100 sq. hektometers =1 sq. kilometer (sq. Km.) =247.114 acres 


When used in measuring land the square meter is called a centare (ca.), the 
square dekameter an are (a.), and the square hektometer a hektare (Ha.). 


Tables THE METRIC SYSTEM 24a 


UNITS OF VOLUME 


Principal unit, the Cubic Meter 


Nore. As the units of volume are cubes whose edges are the corresponding 
linear units, it takes 103 or 1000 units of one denomination to make one of the 


next higher, ; 
TABLE EQUIVALENTS 


1000 cu. millimeters (cu. mm.) = 1 cu. centimeter (cu. cm.) = 0.06102 cu. in. 
1000 cu. centimeters = 1 cu. decimeter (cu. din.) 
1000 cu. decimeters ==) €U. meter (cu...) = 36.314 cu. ft. 


In measuring wood the cubic meter is called a stere (1 st. 0.2759 ed.) ; 
a decister (1 dst.) is one tenth of a stere. 


UNITS OF CAPACITY 


Principal unit, the Liter = a cu. decimeter 


TABLE EQUIVALENTS 
10 milliliters (ml.) = 1 centiliters (cl.) = 0.6102 cu. inch | 
10 centiliters = 1 deciliter (dl.) 
af ‘ 1.0567 liquid quarts 
10 decilit = l ai) 
eciliters 1 liter (1.) | oats dey quate 
10 liters = 1 dekaliter (Dl.) | 
i ; ( 26.417 gallons 
kal == Hl.) = ‘ 
10 dekaliters 1 hektoliter (H1.) 1 2.8875 bushels 
10 hektoliters = 1 kiloliter (I1.) 


The liter is used in measuring hquids and small fruits, the hekto- 
liter in measuring grain, vegetables, and liquids in larger quantities. 


1. With a meter stick find the dimensions of your crayon box. 
How many liters will it hold ? 

2. Observe that a liter (a cubic decimeter) is about the usual size of 
a quart berry-box. This will give a way of changing approximately 
from one table to the other. In apeck of nuts about how many liters ? 

8. Is a barrel (24 bu.) more or less than a hektoliter? At$1 per 
bushel, how much a hektoliter ? 

4. Try to picture a box 1 m. long, 1 m. wide, and 10 cm. deep. 
How many hektoliters will it hold? How many bushels? 


247, | THE METRIC SYSTEM Tables 


UNITS 


OF WEIGHT 


Principal unit, the gram 


TABLE 


EQUIVALENTS 


10 milligrams (mg.) = 1 centigram (cg.) = 0.15432 grain 


10 centigrams 
10 decigrams 
10 grams 

10 dekagrams 
10 hektograms 
10 kilograms 
10 myragrams 
10 quintals 


= 1 decigram (dg.) 
= 1 gram (g.) 

= 1 dekagram (Dg.) 
= 1 hektogram (Hg.) 
= 1 kilogram (Kg.) = 2.20462 pounds 
= 1 myragram (Mg.) 

= 1 quintal (Q.) 

=1 metric ton (T.) = 2204.621 pounds 


= 15.482 grains 


The gram is the weight of a cubic centimeter, the kilogram of a 
cubic decimeter, and the metric ton of a cubic meter of distilled water 


at its greatest density. 


The gram is used in mixing medicines, and in weighing jewels, 


precious metals, letters, etc. 


Ordinary articles are weighed by the 


kilogram (commonly called kilo) and heavy articles by the metric ton. 


TABLE OF EQUIVALENTS 


(FOR REFERENCE) 


Common Metric 

1 inch = 2.54 (cm.) 

1 foot = 80.48 (cm.) 

1 yard = 0.9144, (m.) 
1 rod = 6.029 (m.) 

1 mile = 1.6093 (Km. ) 


1 sq. inch = 6.452 (sq. cm.) 
1 sq. foot = 9.2903 (sq. dm.) 
1 sq. yard = 0.8861 (sq. m.) 
1 sq. rod = 0.2529 (a.) 

1 sq. mile = 2.59 (sq. Km.) 
1. Acre = 0.4047 (Ha.) 

1 cu. inch = 16.887 (cu. cm.) 


Common Metric 
1 cu. foot = 28.317 (cu. dm.) 
1 cu. yard = 0.7645 (cu. m.) 
1 cord = 3.624 (st.) 
1 liquid quart = 0.9463 (1.) 
1 gallon = 8.7185.41.) 
lidry quart) =1.101 Gd.) 
1 bushel = 0.3524 (H1.) 
1 grain = 0.0648 (g.) 
1 ton = 0.9072 (met. ton) 


1 troy ounce “= 31.1035 (g.) 
lav. ounce = 28.35 (g.) 
lav. pound =0.45386 (Kg.) 


Tables THE METRIC SYSTEM 243 


The metric system is not used in this country except in scientific 
work, hence there is lttle need of actually reducing from one 
system to another. That we may be able to form approximate esti- 
mates of lengths, weights, etc., in the English system from length, 
known in the metric system learn the following table : — 


APPROXIMATE EQUIVALENTS 


1 meter = 3 ft. 33 in. 1 liter = 1.06 liq. qt. or 7% dry qt. 
1 kilometer = 3 miles 1 hektoliter = 23 bushels 

1 are = 48g. rd; 1 gram = 15} grains 

l hectare = 2} acres 1 kilogram = 2} ay. pounds 

1 stere = ; cord 1 metric ton= 2200 pounds 


Since the metric system is a decimal system, units may be changed 
to those of a higher or lower denomination by moving the decimal 
point. 

Explain the following changes or reductions : — 


1. 3247.28 m. = 324728 em. = 32.4728 Hm. = 3.24728 Km. = 
3247280 mm. 


Zam (Ob Joresdaciia==s 010.1190) Sq: din, = 6.731796.) sq.m.7— 
0.06731796 sq. Dm. 


8. 8.3724 Ha. = 837.24 a. = 83724 ca. = 83724 sq. m. 
4, 47.234 cu.m. = 47.234 cl. = 47234 cu. dm. = 47234000 cu. em 
Bo 247 Sol We 2AT8el AL = 24783.1 el. 
6. 1346.982 ¢. = 1.346982 Kg. = 134698.2 cg. 
Te oyeiuany mom in aK iin a bimay iin a cm. ? 
8. 25 Ke. are equal to how many pounds to the nearest unit ? 
9. Estimate the length of the room in meters. 
10. Estimate the weight of familiar objects in Kg. 
11. Estimate in cm. lengths of lines drawn on the blackboard. 


12. Give the dimensions of your books, slates, etc., in em. 


2944 THE METRIC SYSTEM Written 


In 847.2 Kg., how many grams ? How many pounds ? 
Change 75 bushels to hektoliters. 
How many square meters in a rectangle 18 ft. by 10 ft.? 


HPSS ORE So he 


An importer pays duty on 1200 meters of cloth. How many 
yards ? . 
5. How many square rods in a square hektometer ? 

6. How many liters in a cubic meter ? 

7. An importer buys 250 1. of liquor at $0.75 a liter. He sells 
it for $3 a gallon. What does he gain or lose ? 

8. A rectangular stone is 1 m. long, 5 dm. wide, and 24 em. thick. 
How many kilograms does it weigh, being eight times as heavy as 
water ? 

9. How many kilograms of flour in a barrel ? 

10. Add 18.32 Km., 648 m., 94.8 Hm., 38.4 dm. 

11. What will a stere of stone cost at $12 a cord ? 

12. How many hectares in a field 14 Hm. long and 40 Dm. wide ? 
How many acres ? 

13. How many gallons in a cubic meter of water ? 

14. How many times is 16 dm. contained in 1.28 Km. ? | 

15. If goods are bought at $2.35 per yard, at what price per 
meter must they be sold to gain 25%? (1 meter = 39.37 inches.) 

16. A hektoliter of fruit weighs 63 kilograms, and 32 liters of 
sirup can be obtained from it. How many kilograms of fruit will 
it take to make a hektoliter of sirup? | « 

17. The distance between two places on a map is 12.5 centimeters. 
What is the actual distance between the places if the scale of the 
nap is 1 to 60,000 ? 

18. Ifa certain stone is 2.83 times as heavy as water, what is the 
weight of a piece of this stone which is 5.39 m. long, 17.386 dm. wide, 
and 52.6 em. thick ? 

19. A stone measuring 5.2 em. by 17.3 cm. by 0.43 m. weighs 7.25 
kgs. How many times as heavy as water is the stone ? 


Oral STANDARD TIME 247 


The local time of the 75th meridian is Eastern Time, of the 90th, 
Central Time, of the 105th, Mountain Time, of the 120th, Pacific Time. 


5. Which time do you use? 

6. When it is 8 a.m. Eastern Time, what is it Pacific Time ? 

7. When it is 4 p.m. Mountain Time, what is it Eastern Time ? 

8. At noon by Central Time, what is it by each of the others ? 

9. If one is traveling from New York to Chicago, how will he 
change his watch as he changes into Central Time ? 


The line of division between standard meridians is not a straight line 
midway between them, but depends upon important railroad terminals. 
It was fixed by the roads. This is shown in the following map. 


WN 


ee 


TR 


D 


10. When it is noon in Chicago, what time is it in New York? 
Charleston ? New Orleans ? 

11. When 3 p.m. in San Francisco, what time is it in St. Louis ? 
Detroit? Boston? 


248 REVIEW EXERCISES ) Oral 


1. 2% of a number is 50. What is the number ? 

2. The area of a trapezoid is 350 square feet. The parallel sides 
are 30 feet and 40 feet. Whatis the distance between them ? 

3. Find the missing term: 6:8=16:2. 

4. The area of a triangle is 25 square feet. Its altitude is 5 feet. 
What is its base ? 

5. The cost of 12 oranges at the rate of 3 for 5¢ is what per cent 
of 80¢? 

6. A boy has 50¢. He told his friend that this was 40% of 
what his books cost him. What was the cost of his books ? 


7. .One boy rides, his wheel 30 miles an hour. Another boy rides 
at the rate of 4 mile in 30 seconds. How far does each ride in a 
minute ? 

8. If I sell 68 yards of cloth to-day, and this is 64% more than 
I sold yesterday, how many yards did I sell yesterday ? 


9. 10 added to 35 is the same as the product of what 2 factors 
less than 10? 


10. An engine ran 25 rods from the engine house, then back 
18 rods, then forward 60 rods. How far from the engine house did 
it stop? Draw a line. 


11. It is 12 in. on a map between two cities. How far apart are 
they if the map is drawn 200 mi. to the inch ? 


12. Interest of $ 234 for 60 da. at 3 per cent is $a. 


13. What per cent is made by buying fish at $6 per hundred- 
weight and selling it at 10¢ a pound? 


14. How much 3% stock must be purchased to yield an annual 
income of $450 ? 


15. A commission merchant charges 5% for selling potatoes at 
60¢ a bushel. His bill is $30. How many bushels did he sell? 


Oral REVIEW EXERCISES 249 


1. If a quart of cream will serve 8 people, how many gallons 
shall I order for 300 ? 


2. A horse harnessed is worth $150. If the harness increases 
his value 20 per cent, what is the harness worth ? 


3. If the working week is reduced from 66 hr. to 60 hr. and 
wages in proportion, what does the $2 man get after the cut? 


4. Flour goes up from $5 to $7. What ought a loaf to sell for 
after the rise if it had previously sold for 10¢ ? 


5. A bankrupt’s labilities are $14,000 and his assets $8000. 
What does the creditor lose who receives $ 400 ? 


6. 15 ounces is 3% of how many pounds? 


7. A man can do a job in two days. A boy can do it in 6 days. 
What shall I pay the boy if the man has $ 2 a day ? 


8. Bought stock at 112 and sold at 98. Loss on 30 shares ? 


9. A mason works 8 hours for $3, and a carpenter 10 hours 
for $3.50. How much does one earn more than the other in 
100 hours ? 


10. 90,000 copies printed in an hour are & copies per second. 


11. What are the proceeds of a 60-day note for $200 discounted 
at date at 9%? No grace. 


12. Of a flock of 1000 sheep 400 die. What must each of the 
remainder be sold for to cover the loss? The sheep cost $8 each. 


13. I carry $36,000 insurance at 3%. Find the premium. 
14. What is the square root of 27? 


15. What is the length of the longest line that can be drawn in a 
rectangle 6 by 8 inches ? 


16. A building lot contains 3382 sq. ft. and is 100 ft. long. How 
wide is it? 


250 REVIEW EXERCISES Oral 


i. Read as per cents: 75, fp Yo Pm > To Tp ap Te 

2. Read as fractions in smallest terms: 125%, 183%, 314%, 
373%) 433% , 565%) 835%) 683%. 

3. Of a mixture 15 gal. of alcohol make 311% of it. How 
many gallons in the mixture ? 


4. Give the cost of :— 


8 at $2 per dozen. 9 at $4 a dozen. 
7 at $2.50 per dozen. 2 at $5 a dozen. 
5 at $1.50 per dozen. 16 at $3 a dozen. 


5. Required the semiannual dividend from $18,000 in 31% 
bonds. 


6. What is the value of a ton of soap in 4 oz. cakes at 48 f a 
dozen ? 

7. How many envelopes can I buy for $12 at 75 ¢ per M? 

8. Bought pencils at $3 per gross and sold them at 60 cents a 
dozen. Gain on 5 gross? 

9. Paid $x for a pair of $8 shoes less two 10% discounts. 

10. Of 300,000 immigrants 40% are illiterate. How many of 
them can read ? 

11. If a half million out of a gift of 3 millions for a hospital is 
spent for the building, what is the annual income from the remainder 
at 31% ? 

12. Each angle of a triangle measures 60°. What kind of triangle 
is 1t? 

13. x ininutes will take a horse 6 times around a 4 mile track if 
he trots at a 2:10 gait. 

14. It is 160 rods round a square field containing «& acres. 

15. What will pay a note of $ 800 that has been running 8 months 
at 6% ? 

16. 121% of 64 is 831% of what? 


Written REVIEW EXERCISES 251 


1. A broker received $75 for purchasing bonds at 1% commis- 
sion. What was the face value of the bonds ? 


2. A man offered to sell his horse for 25% more than it cost 
him. He afterwards sold it for $190 which was 5% less than he 
first asked for it. What did the horse cost him ? 


3. A house cost $3000, and rents for $25 a month. If the 
taxes and other expenses amount to $ 50 annually, what per cent does 
it pay on the investment ? 


4, A man desires to settle an annual income of $700 on his son. 
How much must he invest in U.S. bonds, paying 3£% at 105 to yield 
that income ? 


5. A city map is drawn to a scale of ;4, mile to the inch. What 
is the length of a line which represents a street } mile long? 


6. Mr. Jones kept 75 bushels of cranberries through the winter, 
but found + of them worthless. He sold the good ones for $3.50 a 
bushel, receiving $15 more than he would had he sold them in the 
fall. What was the price per bushel in the fall ? 


7. Ifa gas jet burns 4 cubic feet of gas in an hour, and 4 jets are 
lighted each evening from 6.30 to 10, what will be the gas bill for 
February at 10 ¢ for 100 cubic feet ? 


8. On a certain locomotive the driving wheel 7 feet in diameter 
turns 24,000 times in going from Boston to Springfield. How many 
times will a car wheel 30 inches in diameter turn in going the same 
distance ? 


9. 2 of an article sold for the cost of 7 of it. What was the gain 


per cent ? 


10. I send $ 4935 to a broker in Chicago for the purchase of flour 
at a commission of 5%. If he paid $5 per bbl., how many barrels 
did I receive ? 


11. Sold 1500 lbs. of coal for what a ton cost. Gain = 2%. 


22, REVIEW EXERCISES . Written 


1. When 5% bonds are quoted at 104, what sum must be invested 
to have an annual income of $1600? Brokerage 1%. 


2. Borrowed $500 at 6% on June 10, 1902. When it was paid 
it amounted to $546. On-what date was it paid ? 


3. If the holder of a $150 note running 4 mo. had it discounted 
at a bank July 15, 1903, at 5%, what did he receive? Date, June 5, 
1903. 


4. If the note was unpaid when due, and drew interest at 5% 
from the time it became due, what would settle it March 27, 1904 ? 


5. A young man whose salary is $24.00 a week pays $7.50 a 
week for board and $8.75 a week for other expenses. In how many 
weeks can he save enough to pay a debt of $279? 


6. Received a consignment of 2000 barrels of flour which sold 
at $5.50 per barrel. I paid $74 for storage and $27 for carting. 
How much ought I to remit, after deducting a commission of 4% ? 


7. A sewing machine was sold at a discount of 124% on the 
asking price and at a gain of 40% onthe cost. If the cost was $50, 
what was the selling price? The asking price? 


8. How many feet of wire will be required to fence a square 
field containing 3136 square feet, if there are three rows of wire in 
the fence ? 


9. A hall 20 feet high has a square floor containing 6561 square 
feet. A merchant agreed to furnish burlap one yard wide for the 
walls at 15¢a yard, if the bill was paid on or before Feb. 4, 1903. 
It was not paid until Dec. 22, 1903, when interest was required at 
D%. What amount was required to pay the bill? 


10. A 90-days’ note for $350, dated Nov. 25, was discounted 
Dec. 19. What did the payee receive ? 


11. How many gallons will a standpipe 15 feet in diameter and 
80 feet high contain? One gallon equals 251 cubic inches. 


Written REVIEW EXERCISES 255 


1. A physician received $76 from a collector whose commission 
was 5%. What was the amount collected ? 


2. I pay $13.50 for insuring my furniture at 3%. For how 
much is it insured ? 


3. $16.50 will settle a bill on which the discount is 10% for 
cash. What difference will it make if I delay the payment? 


4. What per cent is made by buying coal at $4.65 a long ton 
and selling it at $8 a short ton ? 


5. After deducting his commission of 4%, how many barrels of 
apples at $1.50 can an agent buy with a remittance of $2000 ? 


6. How much will a broker charge, whose commission is 4 
for selling 85 shares of stock, — par value $5 ? 


7. Shall I increase or diminish my income by selling 80 shares 
of 5% stock at 72 and investing in 8% stock at 108}? 


8. What is the tax on property assessed for $4780 at $16.30 a 
thousand ? 


9. $360 was paid an agent for buying cotton at a commission of 
89. He afterwards sold the cotton at a profit of $4500, deducting 
his. commission of 11%. What was his commission on the selling 
price, and what were the proceeds ? 


10. An agent receives $2184 with which to buy meat at 163 ¢ 
per pound. How many pounds can he buy at a commission of 5% ? 


11. In a city $275,000 was raised from a 14% tax. What was 
the assessed valuation of the property ? 


12. What is the net price of an article listed at $50 and sold ata 
discount of 25, 10, and 4% ? 


13. The surface of a cube is 576 square inches. Find its volume. 


14, Find the exact interest of $250 from July 18, 03, to 
Jan. 5, 704. 


204 REVIEW EXERCISES Written 


1. Find the cost of $500 in U.S. bonds bought at 1264, broker- 
age 3%. 

2. What is the per cent of profit if I buy oranges at $1.50 a 
hundred, lose 10% of them by decay, and sell the remainder at the 
rate of 3 for 10 cents ? 


3. The proceeds of a 90-day note, discounted at a bank at date, 
were $492.50. What was the face of the note ? ; 


4. What premium must be paid on a building valued at $7500 
and insured for 2 of its value at 4% ? 


5. A man can do a piece of work in 3 days. His brother can do 
it‘in 4 days. What part of the work does each do in a day ? 


6. What part would both do in a day working together? If 
they work together, how long will it take them to do the work ? 


7. A farmer can mow a field in 10 hours. His hired man 
requires 12 hours to mow the same field. Suppose they work 
together, how long will it take? 


g. A can doa piece of work in 6 days, B can do it in 8 days, 
and C can do it in 12 days. How long will it take the 3 men work- 
ing together to do the work ? 


9. Three men can paint a boat in 4 days. Two of ‘them can do 
it in6days. How long would it take the third man working alone ? 


10. A lot is 200 feet by 90 feet. A house, the main part of which 
is 24 feet wide and 42 feet long, with an ell 14 by 20 feet, is built 
upon the lot. <A cellar 8 feet in depth is dug under the whole 
house, and the soil used in filling the rest of the lot. How deep 
was the filling ? 


11. I have $15,000 to invest. Which had I better do, buy 8% 
stock at a premium of 50, or loan the money at 5}% interest ? 


12. Required the amount of a note for $628 on interest from the 
4th of July, 1903, to May 30, 1904, at 53%. 


Written 


1. Find the 


Sum of: —— 


$ 467.95 
784.87 
591.23 
467.89 
321.10 
456.78 
432.19 
567.89 
987.65 
439.87 
420.65 
398.76 
987.65 
849.77 
976.93 
842.67 
649.34 
897.66 
307.95 


REVIEW EXERCISES 255 


2. A cubical bin is 100 inches long. How many 
cubic feet does it contain ? 


3. A lot of land rectangular in shape is 186 feet 
long and 151 feet wide. What is its value at 163 
cents a square foot ? 


4. An automobile was sold for $600 at a loss of 
20%. What would have been the gain or Jose per 
cent if it had been sold for $800 ? 


5. Find the interest of a half million dollars at 24% 
for 111 days. 


6. What can I secure at a bank for a ninety-day 
note for $2200, the rate of discount being 5 per cent ? 
No grace. 


7. Draw an equilateral triangle. Draw a line repre- 
senting its altitude. Calling the side of the triangle 
50 feet, what is its altitude to the nearest hundredth 
of a foot? 


8. I am obliged to pay three months’ interest at 7 
per cent on my tax bill. The rate is $16.70 per thou- 
sand, and my property is assessed for $18,600. What 


shall I be obliged to pay in all? 


9. A man bought a house for $2500 and sold it for $1875. 
What per cent of the cost did he lose? 


10. What is the interest of $320, at 6 per cent per annum, from 
Jan. 2, 1903, to Nov. 20, 1905 ? 


11. A merchant sold goods for $240, thereby losing 20 per cent 


of the cost. 


15%? 


For what amount should he have sold them to gain 


12. A note for $800, dated May 1, 1900, falls due Aug. 17, 1908. 
What will settle it if it draws 4 per cent interest ? 


256 REVIEW EXERCISES Written 


1. I am offered a $40 suit for $35, or a $35 suit for $30. 
Which is the better offer and why ? 


2. A note for $750 dated October 19, 1903, drawing 4 per cent 
interest, falls due May 17, 1904. What will settle it ? 


3. It costs $120 to fence a square lot at $2 arod. What is the 
land worth at $1600 an acre ? 


4. I buy tea, pay an ad valorem duty at 25 per cent, and double 
my money by selling at $1.00 a pound. Required the cost without 
duty. 


5. A train running 50 miles an hour is 86 minutes in going from 
one station to another. How far apart are the stations ? 


6. A note for $800, drawing 5% interest for 18 months, is 
discounted by a bank 90 days before maturity, at 7%. Required 
proceeds. 

7. By selling a farm for $4800, the owner lost 4 of what he paid 
for it. Find the per cent of loss. 


8. The discount on goods at 30%, 10%, and 5% off is $23.94. 
What is the list price ? 


9. What sum of money at 5% simple interest will produce in 
one year and three months the same interest that $2940 will pro- 
duce at 4% in two years and six months? (Solve by proportion.) 


10. The square on the diagonal of a square room is 648 sq. ft. 
What will it cost to carpet the room with carpet 3 yd. wide, at 90¢ 
a yard ? 


11. What must be paid for stock paying an annual dividend of 
3% to secure an annual income of 7% from the investment ? 


12. The proceeds of a note for $500 discounted at 6% are $492.50. 
Find the term of discount. 


13. In what time will a sum of money double itself at 8%? 


14. Draw a line 0.0001 of mile long. 


Written REVIEW EXERCISES D5¢ 


1. After spending 2 of his money in travel and 4 of the remain- 
der, Mr. Emerson finds he has $440. He had «& dollars at first. 


2. When $14 will buy a gallon of oil, how much will $3 buy ? 


3. A tank containing 480 gallons is emptied by two faucets in 
5 and 7 minutes; respectively. How much water will pass through 
each, if both are open at once ? 


4. A rectangular cistern contains 2941 cu. ft. of water and meas- 
ures 133 ft. x 6 ft. x aft. Value of «? 


5. A garden roller is 44 ft. long and 64 ft. in circumference. 
How much surface will it pass over in 48 revolutions ? 


6. At $40 per M, what will be paid for 6 boards 16 ft. long and 
in width tapering from 20 in. to 15 in. ? 


7. Invested $26,250 in N.P. bonds at 874 and sold them the 
next day at 91. I gained @ dollars. 


8. How many times larger is a 100-ft. circle than a 50-ft. circle ? 


9. If a man is satisfied with 34% of his investment, what can 
he afford to pay for U.S. 4’s ? 


10. The Boston Journal is printed from rolls of paper 64 in. wide. 
Each page is 16 x 22.. If 160,000 copies of 8 pages each are printed 
daily, how many miles of 64 in. paper are required ? 


11. Two trappers have provisions for 9 months. If A had been 
away, they would have lasted B 12 months. They would have 
lasted A alone # months. 


12. If 24 men can mow 66 acres in 2 days, how many acres can 
14 men mow in 7 days? 


13. What is the interest of $248 for 6000 days at 74%? 


14. Mr. Green purchased a $40 suit at 10% discount and yet the 
dealer made 25%, for it cost him only # dollars. 


258 REVIEW EXERCISES Written 


1. James B. Chase buys of John R. Knight, Nov. 30, 1908, 
goods to the amount of $600, for which he gives his note payable in 
3 months, without interest. On Dec. 30 Mr. Knight sells the note 
to a bank at a discount of 5%. What sum does he receive ? 


2. Write the above note as it will appear after the bank gets it, 
making your town or city the place of the transaction. 


3. If 1 of a grocer’s cash sales are profit, what is his profit 
5 § p p 
per cent ? 


4. The extremes of a proportion are 49 and 196, and the means 
are equal to each other. What is the proportion? Explain the 
operation. 


5. Two kinds of silk are sold, each at $3.60 a yard. On one 
kind the merchant makes a profit of 334%, and on the other 331% 
of the selling price is gain. On which does he make the greater 
gain, and how much per yard ? 


6. A dealer buys oats at 42¢ a bushel. In selling he makes a 
profit of 162%, which was a reduction of 123% from his asking 
price. His asking price was a ¢. 


7. What income will be derived semiannually by investing 
$8214 in 4% R.R. stock at 26% below par ? 


8. What must be the depth of water in a cylindrical cistern 
2 ft. 6 in. in diameter to contain 153 gallons ? 


9. Received a remittance of $25,375 for the purchase of cotton 
at 121¢ a pound; this included my commission of 14%. I bought 
x pounds. 


10. May 14, I get a 90-day note for $1292 discounted at 6%. The 
note was dated April 10, 1903. Proceeds ? 


11. If it costs $520 to fence a rectangular lot 120 rods x 80 rods, 
what will it cost to fence an equal square lot at the same rate ? 


Written REVIEW EXERCISES 259 


1. In 1860 there were 40 high schools in the United States. In 
1900 there were 6005. What was the per cent of increase ? 


2. Pure water weighs a thousand ounces to the cubic foot. 
Dead Sea water weighs 77 pounds to the cubic foot. What per 
cent of impurities in the latter ? 


3. The tire of a wheel on a watering-cart is 6 inches wide. If 
the wheel is 5 feet in diameter, what surface of ground is covered at 
each revolution ? 


4. Merchandise may be sent 3000 miles by mail for 1¢ an ounce; 
by express the charge is $1.25 a hundred. What will it cost to 
send 75 pounds in the cheaper way ? 


5. A tax of $6971.60 is to be assessed upon a town containing 
430 polls, taxed at $1.25 each. Its real estate is valued at $ 1,354,- 
000 and its personal property at $75,000. Find the tax of a man 
whose property is assessed at $3640 and who pays for one poll. 


6. A person borrows $100, and at the end of each year he pays 
$25 which goes to reduce the principal, after paying interest at 4% 
on what he has owed during the year. How much does he owe at 
the end of 3 years ? 


7. A man having $2655 invests it in 34% bonds at 881. After- 
ward, when they are 93, he sells out and invests his money in a 54% 
mortgage. What difference has he made in his income ? 


8. The total expense of maintaining the schools in a certain city 
is $287,000. If the school keeps 40 weeks, 5 days in a week, and 
there are 10,500 school children in the city, what is the cost of each 
day’s schooling for each child ? 


9. The inside diameter of a hollow sphere is 7 in. The thick- 
ness of the shell is 31 in. Find the volume of the shell. 


10. Required the proceeds of a 4-mo. note for $5000, discounted 
at 54% 37 da. after date. 


260 FROM EXAMINATION PAPERS Written 


1. What per cent of discount lets a $225 horse go for $1855? 


2. Which produces the greater per cent of income and how much, 
5% bonds at 120 or 4% bonds at 105 ? 


3. After my bill has been reduced by successive discounts of 
20% and 10%, I can pay it for $1016.64. What was the gross 
amount charged ? 


4. What is the rate of duty on jewelry if $402.50 is charged on 
an invoice of $1150? 


5. A savings bank pays 4% interest compounded semiannually. 
A man makes a deposit of $50 every six months beginning July 1, 
1901. What amount stands to his credit Jan. 1, 1903? 


6. The successful candidate received 6750 votes. His opponent 
had 3825. How were every 100 votes divided ? 


7. What is the exact interest of $81 from Dec. 31, 1902, to 
March 12, 1903, at 6% ? 

8. What is the tax rate of $1 where $73,000 is to be raised 
on a valuation of $5,309,090 ? 


9. The last reading of my gas meter was 67,300 cu. ft. The 
previous reading was 64,900. At $1.50 per thousand, with a dis- 
count of 15¢ per thousand cu. ft., my gas bill was # dollars. 


10. Find the square root of 2, correct to thousandths. 


11. A rectangular field is 64.8 rods long and 36.05 rods wide, and 
a square field is of equal area. At $1.10 a rod, how much more will 
it cost to fence one than the other ? 


12. I bought 1185 lb. of hay at $19.50 per ton, for x dollars. 


13. Solda7% mortgage for $3000 at 25% premium, and bought 
6% railroad stock at par with the proceeds. Did I increase or lessen 
my income? 

14. One third of the sum of two numbers is 384, the difference is 
64. What are the numbers ? 


Written FROM EXAMINATION PAPERS 261 


1. I bought a house for $2500, and sold it so that 20% of the 
selling price was profit. What did I receive for it ? 

2. % yd. carpeting is used for a room 20 ft. square. The waste 
in matching is 6 in. toa strip. The cost at $1.75 per yard is $a. 

3. The wheels of a bicycle are 30 in. in diameter; the gearing is 
such that each wheel makes two revolutions to every turn of the 
pedals. How many times will each pedal turn in a ride of one mile ? 


4. Mr. Brown is taxed on w.dollars. His tax bill is $110.00, 
including $2 for poll tax, the rate being 9 mills on the dollar. 


5. A horse and wagon were sold for $120 each; the horse was 
sold at a loss of 25%, the wagon was sold at a gain of 25%. Find 
how much was lost or gained on the whole transaction. 

6. Bought railroad stock at 1143, and sold at 1171. In each case 
I paid 4% brokerage. What was my profit on 200 shares ? 

7. My broker bought for me 26 shares of stock at 107 and sold 
them for 1187, brokerage in each case £%; find my gain. 

8. Which is the better investment, 5% stock at 120, or 6% at 
150 ? 

9. If 2 of a day’s wages are $1.40, what shall be paid for ;% of a 
day ? 

10. A man fails and pays 67 cents on a dollar; after paying his 
lawyer’s fee of 4%, how much would a creditor receive on a claim of 
$ 625 ? 

11. I bought cloth by the meter (59.37 in.) and sold at the same 
price per yard. What per cent did I gain? 

12. A garden 145 feet long and 120 feet wide is inclosed by a 
tight board fence 6 feet high; find the cost at 8” a square yard, of 
painting both sides of the fence. 


13. Find the surface of a sphere 25 inches in diameter. 


14. How many square inches are left of a sheet of paper 14 in. by 
21 in. after the largest possible circle is cut out of it ? 


962 FROM EXAMINATION PAPERS Written 


Pipa Par a Na oat 
1. Simplify Go oe. 


2. How far is a man from the starting-point, who travels west 
48 miles then due north 62 miles, and then east 14 miles ? 


3. Sold my carriage at 3% gain, and with the money bought 
another which I sold for $182 and lost 124%. What did each car- 
riage cost ? . 

4. A 90-day note for $ 500 without. interest, dated December 10, 
1904, will yield what proceeds if discounted at 6% Jan. 10? 


5. A man borrowed $2700 November 11, 1903, with interest at 
5%; find the amount of his debt Aug. 5, 1905. 

6. Find the difference in a bill of $825 between a discount of 
25% and a discount of 10%, 10%, and 5%. 


7. The distance around a rectangular field whose width is ? its 
length, is 98 rods; find the area of the field. 


8. A dealer obtained $480 for a piano, the Tat price of which he 
had discounted 50%. He still made a profit of 20%. At what was 
it listed ? What did it cost him ? 


9. Bought $15,000 worth of goods on 4 months’ time, and sold 
immediately for $14,900 cash. Money being worth 5%, what did I 
gain ? 

10. Find the cost at $20 a ton of 12 bales of hay averaging 218 
pounds each. 


11. What sum will cancel a 5% note for $763, dated April 19, 
1901, and maturing Aug. 11, 1904 ? 


12. An article sells for $1.29; if the profit is 50%, what was the 
cost ? 


13. 4% government bonds yield an annual income of $1000. 
What is their face ? 


14. $120 yields $8 annually. What rate per cent is this ? 


Written FROM EXAMINATION PAPERS 263 


: ‘ .  8+2)x @-% 
1. Simplify the following: DES Fac cS aaape 

2. How many gallons in a cylindrical can 2 feet in diameter and 
3 feet deep ? 

3. William Snow bought this day of John West for cash the 
following: 4 lb. tea at 45 cents, 2 lb. coffee at 40 cents, 2 bushels 
potatoes at 50 cents, 25 lb. sugar at 5 cents. Make a receipted bill. 


4. Each side of a triangle measures 30 feet. Its area is a. 


5. A bookseller buys books from the publishers at 40% off the 
list price. He sells a set of Thackeray’s works which list at $30 at 
a discount of 20%. What per cent does he make ? 


6. Hats bought at $15 a dozen are sold at $2 apiece; find the 
gain per cent. 

7. Find the amount of $585 at simple interest for 1 year, 5 
months, 17 days at 53%. 

8. Bought Lats at $27 a dozen and sold them at $3.75 each; 
find the gain per cent. 

9. At $6 a thousand, find the cost of shingles laid 4 inches to 
the weather to cover a roof of 1750 square feet, the shingles averag- 
ing 4 inches wide. 

10. At what price must stock paying 4% be bought in order that 
5% may be realized on the investment ? 

11. Find the proceeds of a bank-rfote for $650 discounted for 
90 days at 6%. 

12. A house and lot cost $5000; the insurance is $25, taxes are 
$ 50, and repairs $75 annually; what rent must be received in order 
to realize 6% on the investment ? 

13. Find the cost of the following lot of lumber: — 

20 pieces 13 ft. x 6 in. x 10 in. at $14 per M. 
10 pieces 16 ft.x 2in.x 4 in. at $16 per M. 
6 pieces 24 ft. x 8 in. x 10 in. at $15 per M. 


264 FROM EXAMINATION PAPERS Written 


1. Reduce the following to its simplest form : 


2. Find the amount of $486.50 for 1 year, 5 months, and 17 
days at 44% simple interest. | 

3. A man 6 feet high casts a shadow 42 inches long. Find the 
height of a flagstaff which at the same time casts a shadow 28 feet 
long. 

4. Find the proceeds of a note for $560 discounted for 90 days 
at 3£%. 

5. How many times will a wheel 4 ft. in diameter revolve in 
going one mile ? 

6. Find the cost of 6 pieces of timber each of which is 32 ft. 
long, 10 in. wide, 8 in. thick, at $14 a thousand feet, board measure. 


7. Ona bill of goods amounting to $485.50 I received commercial 
discounts of 15%, 10%, and 5%. Find the net cost of the goods. 
8. What is the market value of 25 shares of New York Central 
stock at 46% premium ? 
9. 4% government bonds yield an annual income of $1400. 
What is their face ? 
10. The cost of 50 gallons of molasses is $25. If 1 is lost by 


leakage, and 20 gallons are sold at 624¢ a gallon, at what price per 
gallon must the remainder be sold to gain $5? 


11. At 21% discount, what shall be paid for 4% stock so that the 
annual income shall be $2400 ? 


12. Find the proceeds of a note for $3000 at 69 days when dis- 
counted at 5%. 


13. The diagonal of a square field is 20 rods. What is its 
perimeter ? | 


14. A field is 42 rods long and 35 rods wide. Find its value at 
$37.50 an acre. 


Written FROM EXAMINATION PAPERS 265 


Pasay eae 
1. Reduce fe uch to a simple fraction in its lowest terms. 
42 x 53 
2. I sell an article at an advance of 25% on the cost and then 
discount the bill 5% for cash payment. My net gain is $63.75. 


Find the cost. 


3. Hind the cost of 8 sticks of timber each 42 ft. long, 10 in. 
wide, 8 in. thick, at $18 per M, board measure. 

4. An agent received $32 as his commission at 4% for buying 
flour at $5 a barrel. How many barrels were bought ? 

5. Find the cost, at $28 per M, of lumber for a floor 21 feet 
long by 16 wide, allowing } of the lumber for matching. 

6. Find the cost of the following bill of goods: 1840 lb. hay at 


$14 a ton; 2460 lb. coal at $5 a ton of 2240 lb.; 5120 lb. oats at 
24 cents a bushel of 32 lb. Make and receipt the bill. 


7. A plot of ground in the form of a triangle contains 2 acres of 
land; the base of the triangle is 40 rods. Find the altitude. 


8. An agent remits to me $247.38 after retaining a commission 
of 5% for collection. What sum did he collect? What was the 
amount of his commission ? 

9. If a square field contains 10 acres, what is the length of the 
diagonal ? 

10. Find the cost of papering the walls of a hall 36 feet long, 
24 feet wide, and 18 feet high, with paper 14 feet wide at $0.25 a 
roll of 16 yards, allowing 64 square yards for doors and windows. 


11. A house was sold for $1850 at an advance of 15% on the 
cost. What would it have brought at a gain of 20% ? 

12. Sold 2 of an article for what 3 of it cost. What was the gain 
per cent ? | 


13. What per cent would I receive on my investment if I should 
buy at 10% discount stock which pays an annual dividend of 44% ? 


266 FROM EXAMINATION PAPERS Written 


1. The owner of 3 of a mine sold ;% of his share for $40,500. 
What should he who owns 3 of the mine ne for 2 of his share ? 


2. A bookseller buys a one whose catalogue price is $3.50, at 
a discount of 20% and 5%, and sells it at 10% above the re 
price. What per cent profit does he make ? 


3. A farm costing $3500 sold for $5400. What was the per 
cent of gain ? 

4. A coal-bed 10 feet thick covers a square mile. How many 
15-T. carloads, allowing 45 cu. ft. to a ton? 

5. How many acres in a street 11 miles long and 4 rods wide ? 


6. I buy apples at $2 a barrel and lose 20% of them. At what 
price per barrel must I sell the remainder to gain 10% on the 
transaction ? 


7. At what price must I buy stock that pays annual dividends 
of 8% in order to realize 44% on my investment ? 

8. I sell goods at 15% below the marked price and still make a 
profit of 10%. What per cent above cost was the marked price ? 


9. A owns $ of a manufacturing plant. The plant is valued at 
$48,870. <A cells a part of his interest for $10,860. What part of 
his interest does he sell ? 


10. A certain stock pays 10%. At what rate must it be bought 
to yield 6% on the investment ? 


11. How many bushels of oats will be contained in a bin 30 feet 
long, 15 feet wide, and 10 feet deep ? 


12. Sold a horse so that + of the gain equalled ;% of the cost. 
What was the gain per cent ? 


13. A square field containing 274 A. has a diagonal path across it 
« rods in length. 


14. Find the cost of 8246 lb. of coal at $5.50 a ton of 2000 lb. 
15. When $ 3460 is a loss of 20%, $a would be a gain of 20%. 


Written FROM EXAMINATION PAPERS 267 


344 21-11 


& x 18 


1. Simplify the following: + 1.375, 


2. I paid $25 for linoleum, at $1.25 per square yard. The 
length of my floor was 15 ft. What was its width? 

3. From a field containing 50 acres I sold a corner 100 rods long 
and 40 rods wide. What per cent remained ? 


4. By selling stock at 84 there is a gain of 5% on the invest- 
ment. At what price was the stock purchased ? 


5. Find the contents in bushels of a bin 8 feet long, 4 feet wide, 
and 6 feet deep. 

6. A merchant buys goods for $1125. He sold 4 at an advance 
of 25% on the cost, ? at an advance of 124%, and the remainder at 
one half their cost. What was his profit ? 


7. Find the cost of 20 boards, each 14 ft. long, 8 in. wide, and 
14 in. thick, at $24 per M. 

8. What will it cost to cement a cellar bottom 36 ft. long, 23 ft. 
7 in. wide, at 96 a square yard? 


9. A merchant bought 3 yards for $2 and sold 2 yards for $3. 
What was his gain per cent ? 


10. Bought 240 barrels of apples at $1.75 a barrel; lost 40 bar- 
rels through frost. At what price a barrel must I sell the remainder 
to gain 25% on the money invested ? 


11. A coat cost $8. How shall it be marked that the dealer 
may lower the price 20% and still gain 20% ? 

12. Find the face of a 60-day note which, when discounted at a 
bank, will yield $250. 

13. A tree 100 feet high casts a shadow on level ground 75 feet 
long: How far from the end of the shadow to the top of the tree ? 


14. Find the cost of a stone walk 4 rd. long and 5 ft. wide at 60 
cents a square foot. 


268 - FROM EXAMINATION PAPERS Written 


1. Make a receipted bill for the following : — 


Bought of Dyer & Co. for cash: 34 lb. of tea at 45 , 20 lb. sugar 
at 51 ¢, 2 lb. coffee at 50 ¢, 10 yd. of muslin at 73 ¥. 


2. I buy oranges at the rate of 15 cents a dozen, and sell them at 
the rate of 3 for 10 cents; find the gain per cent. 


3. At 8 cents a foot, what will be the cost of a board 12 ft. long, 
10 inches wide at one end, and tapering to a point ? 


4. If 14 quarts of grass seed are required for an acre of ground, 
what will be the cost of the seed for a field 36 rods by 24 rods, the 
seed being worth $ 33 a bushel ? 


5. School bonds bearing 41% interest sell at 10% premium; 
what rate per cent does the buyer get on his investment ? 


6. Leaving 3 of my money at home, I spend 5% of the rest for 
eggs that cost me 29 cents a dozen. I bought eggs enough to fill 8 
baskets, 5 dozen to the basket. How much money had I at first? 


7. Find the cost at 25 cents a rod, of building a fence around a 
square field of 10 acres. 


8. I sold two cows at $45 apiece. On one I gained 20%, and 
on the other I lost $17.50. For what should I have sold the two to 
have gained 54% ? 


9. Find the amount of $3875 for 11 months 17 days, at 44% 
simple interest. 


10. A field of 18 acres produces 26 bushels of wheat per acre; 
each bushel of wheat makes 52 lb. of flour; if 196 lb. of flour are 
worth $5, what is the value of the crop? 


11. The list price of a carriage is $260. I am allowed 20% and 
10% discounts. What is the net price ? 


12. The net price of a mowing machine is $ 158.40, and the trade 
discounts are 20% and 10%. Find the list price. 


Written FROM EXAMINATION PAPERS 269 


1. Simplify } of “ +2 x 14, 


2. I buy stocks at 4% discount and sell at 4% premium; what: 
per cent profit do | make on the investment ? 

3. A house rents for $40 a month, the annual expenses on it are: 
taxes $92.50, water rate $ 20, and repairs $60. The landlord has 
5% clear profit. What did he pay for the house ? 


4. What must be the length of a field 88 feet wide containing 
one third of an acre? 

5. After buying some goods, a merchant lost 20% of them by 
fire. He sold the remainder at a gain of 331%, receiving $ 250.75 
more than he paid for the whole. What did the goods cost ? 

6. I buy a lot of land at $250 an acre. I divide it into building 
lots 66 ft. x 99 ft., and sell these lots at $400 each. Find the gain 
per cent. 

7. What will it cost to paint the walls and ceiling of a hall 48 
feet long, 27 feet wide, 18 feet high, at 95 cents a square yard ? 

8. At $31 a cord, a pile of 4-ft. wood 32 ft. long cost $ 174. 
How high was the pile? 

9. On an article listed at $ 8, a trade discount of 20%, 10%, and 
5% is made; find the selling price. 

10. Multiply 3 and 15 thousandths by one and five thousandths. 
Divide the product by five million, and express the result in words. 

11. A grocer bought 75 lb. of soap at 61 cents a pound. While 
on hand it dried away 1 in weight. He sold it at 84 cents a pound. 
What was his gain or loss per cent ? 

12. I retail oranges at 3 cents each, gaining 150% on the purchase 
price. What did the oranges cost a dozen ? 

13. A man bought a pair of horses for $ 400, which was 20% less 


than their real value, and sold them for 25% above their real value. 
What was the selling price ? 


270 FROM EXAMINATION PAPERS Written 


wi x 72 
83 — 6h. 
2. Find the cost at $7 per 100 square a of slating a trapezoid 
of which the parallel sides are 64 feet and 32 feet and the perpendicu- 
lar distance between them is 20 feet. 


1. Simplify and express decimally ~ 


3. Find the cost of the shingles required to cover a roof 40 feet 
long, 20 feet wide, at $5 a thousand, if it requires 36 shingles to 
cover 5 square feet. 


4. A box 6 ft. long, 4 ft. wide, and 3 ft. deep is full of oats. 
What is the value of the oats at 30 cents a bushel? 


5. Find the cost of paving and curbing one mile of street, the 
paving being 30 feet wide and costing $2.75 a square yard and eath 
line of curbing costing 30 cents a linear foot. 


6. Find the result of 1.76 x 49.647 + 0.0088. 


7. The interior of a rectangular tank is 24 feet by 3 feet by 
5 feet; in how many minutes will this tank be filled by a pipe that 
admits 18 quarts of water a minute? (1 gallon = 231 cubic inches.) 


8. How many gallons of water in a teh i! cistern 4 ft. 4 in. in 
diameter, the water 16 feet deep ? 


9. Find the ratio of lighting surface to floor surface in a room 
30 by 35 ft., with 4 windows, each 3 ft. by 8 ft. 9 in 


10. A merchant sold a case of goods which cost $14.40 at 10% 
below the marked price, thus gaining 25% on the cost; find the 
marked price. 

11. Find the cost of the ties and rails for 1 mile of single track 
railway, the ties being placed 2 feet apart from center to center and 
each rail weighing 90 lb. a yard, if the ties cost 40 cents each and 
the rails cost $29 a ton of 2240 lb. 


12. A man bought Pacific R.R. bonds at 107, sufficient to give an 
annual income of $252 at 6%. What did he pay for them, broker- 


age 1% ? 


Written FROM EXAMINATION PAPERS 271 


1. Change 53%, and 8 to decimals, and divide the first decimal by 
the second. 


2. Find the cost of carpeting a room 15 feet long, 12 feet wide 
with carpet 27 inches wide, at 75 cents a yard. 


3. A bookseller buys a book whose catalogue price is $3.50, at a 
discount of 20% and 5%, and sells it at 10% above the catalogue 
price. What per cent profit does he make ? 


4. Find the square root of 6,115,729. 


5. A dealer bought 100 bushels of potatoes at 40 cents a bushel. 
If he lost 80% of them, at what price per bushel must he sell the 
remainder to gain 20% on his investment ? 


6. What is the value at $5 a cord, of a pile of wood 4 feet wide, 
10 feet high, and 20 yards long ? 


7. A man endowed a professorship with a salary of $2000 per 
annum. What sum must he invest at 6% to provide this salary ? 


8. A grocer pays $12 for 5 bushels of cranberries, and sells them 
so as to gain 334%; find the selling price per quart. 


9. A pupil who attends school 68 days during a term was marked 
85% for attendance. How many days was he absent ? 


10. John Hartford borrows this day of Charles Smith $280, giv- 
ing his note for 5 months at 5%. Write the promissory note in 
proper form and find its amount at maturity. 


11. Ifa cubic foot of iron weighs 500 lb., what will a cannon ball 
6 in. in diameter weigh ? 


12. Find the exact contents in cubic yards of a solid wall 8 feet 
high and 18 inches thick around a rectangular court 20 yards by 
32 yards. 


13. A’s farm is 240 rods wide; he sells 18 acres off one end. How 
much shorter is his farm than it was before ? 


DT? FROM EXAMINATION PAPERS Written 


1. Simplify [(142 + 43) — (68 x 22)] x .0625. 


2. The owner of 2 of a mill sold % of his share for $4,060. 
What should he who owns 2 of the mill get for ? of his share ? 


3. Ona note of $400, at 6%, dated Jan. 12, 1901, the following 
payments were made: May 22, 1901, $200; Oct. 2, 1903, $150. 
Find the amount due Dec. 10, 1904. 


4. Find the cost at 75 cents a square yard of paving a circular 
court whose radius is 40 feet. 


5. A capitalist buys U.S. 4% bonds to the amount of $50,000, 
par value, at 1123, brokerage 4%. Find the cost of the bonds and 
the rate of income on the investment. 


6. Find the cost of the following lot of lumber : — 


3 pieces 8 in. x 6 in. x 12 ft. at $17 per M. 
30 pieces 12 in. x 2 in. x 14 ft. at $20 per M. 
20 pieces 10 in. x 7 in. x 16 ft. at $25 per M. 


7. A certain house was built by 40 workmen in 48 days, but 
being burned, it is required to rebuild it in 30 days. How many © 
men must be employed ? 


8. A man pays $75 for insuring his house for # its value at 
11%. Find the value of the house. 


9. When chairs are sold for $4.80 a dozen, with a discount of 
5% for cash, what is the cash value of 200 chairs ? 


10. Anote for $350, at 5% simple interest, was given Nov. 23, 
1902. Find the amount of this note June 15, 1904. 


11. A speculator buys bonds whose par value is $10,000 at 1133, 
and sells them at 1151. How much does he gain if brokerage is 1% 
in each transaction ? 


12. Find the proceeds of a note for $425 at 90 days, when dis- 
counted at 31%. 


Written FROM EXAMINATION PAPERS OTS 


1. Simplify @+4x3)+G+8 x 4) — (0.59 + 4). 

2. The ice on a circular pond is 2 feet thick. If the pond is 
1000 feet in circumference, how many cubic feet of ice does it 
contain ? 

3. A yard is 84 feet long and 80 feet wide. What is the length 
of a clothes line that will reach from one corner to the other corner 
diagonally opposite ? 

4. A man sells 2 horses for $200 each; on one he gains 25%, 
and on the other he loses 20%. Does he gain or lose on both, and 
how much? 

5. Make a receipted bill for the following: William Stone buys 
this day of Flagg Bros., 2 barrels of flour at $5.50, 20 lb. sugar at 54 
cents, 4 lb. coffee at 35 cents, 5 lb. butter at 28 cents, 2 bushels 
potatoes at 45 cents. 

6. Change 342% to its lowest terms. 


7. Find the cost of paving a circular court 42 feet in diameter 
at 624 cents a square yard. 


_ 8. The gross amount of a bill of goods is $750.35, and the rates 
of discount are 10%, 10%, and 5%. What is the net cost to the 
purchaser ? 

9. When the duty on a quantity of lace at 30% ad valorum was 
$115.80, what was the cost of the lace, and the duty in frances at 
$ 0.193 per franc ? 

10. A tax of $6750 is levied on a certain village whose assessed 
valuation is $4,500,000. What is the tax on a house assessed at 
'B 8500 ? 

11. Change 4% to the form of a decimal, and multiply it by 0.035. 

12. A man gave away ¢ of the books in his library, lent + of the 
remainder, and sold 4 of those left; he then had in his possession 
360 books. How many books had he at first ? 

13. A house rents for $30 a month, and the owner pays $75 a 
year for taxes and repairs. What is the value of the house if his 
net profit is 5% per annum? . 


9T4 FROM EXAMINATION PAPERS Written 


(FX 25) + (BX 15) + GX FG, 
2 of (¢— ye) xX A— 8) 


1. Simplify 


2. How many tons of coal can be put into a bin 12 feet square 
and 6 feet high, allowing 55 lb. of coal to a cubic foot and 2240 lb. 
to the ton ? 


3. Multiply three and fifteen ten thousandths by one and one 
hundredth, and divide the product by four and five hundredths. 
Express the result in words. 


4. Find the cost of carpeting a floor 134 feet by 18 feet, the 
carpet being 3 of a yard wide and costing $1.20 a yard. 


5. The list price of a bill of goods is $120; find the net cost 
when the successive commercial discounts are 20%, 10%, and 5%. 


6. A physician whose charges are $2 a visit, made on an 
average 5 visits per day in a year of 365 days. He collected 55% 
of his charges and saved $2 out of every $ 5 collected. At this rate 
how much did he save in 2 years and 6 months ? 


7. At what price must I buy 5% bonds in order to get 4% on 
my investment ? 


8. Owing to a deficiency in the appropriation bill, the salaries 
of the clerks in a bureau were reduced 18% for the last quarter of 
the fiscal year. How much did a clerk who was paid $ 287 for the 
last quarter receive during the whole fiscal year ? 


9. At 3 bushels an acre how many bushels of seed oats will be 
required for a field 660 feet long and 462 feet wide ? 


10. A merchant asks for successive discounts of 15% and 5% on 
a bill of $850, but he is offered instead discounts of 10% and 10% ; 
find the difference between the two net amounts. 


11. What is the loss on 40 shares of stock bought at 109% and. 
sold at 1063, brokerage being 4% in each case? . 


Written FROM EXAMINATION PAPERS B10 


SE. abl O\23° 5 

1. Simplify Tz— 9s + 44, 

2. A house was sold for $7050 at a loss of 6%; for what price 
should it have been sold to gain 15% ? 


3. Find the net proceeds on the sale of 576 barrels of flour at 
$7.50 a barrel, the commission being 34% and the freight and 
storage being 33¢ a barrel. 

4. At what price must 5% bonds be bought to realize 7 4% on 
the investment ? 

5. I buy oranges at 8 cents a dozen and retail them at the rate 
of 2 for 3 cents; find the per cent profit. 

6.. Find the cost at 45 cents a roll, of papering the walls of a 
room 164 feet long, 15 feet wide, and 12 feet high, making no allow- 
ance for openings. (A roll of paper is 8 yards long and 18 inches 
wide.) 

7. Received 6% dividend on stock bought at 25% below par; 
what rate of interest did the investment pay ? 


8. Find the cost of the following bill of lumber: 20 scantlings 
14 ft. long, 4 in. wide, and 3 in. thick at $30, per M; 16 planks 10 ft. 
long, 14 in. wide, and 2 in. thick, at $56 per M. 

9. If 54 bushels of wheat cost $4.75, how much will 82 bushels 
cost ? 


10. A merchant buys cloth at $1.20 a yard, and: marks it so as to 
sell it at a discount of 20% from the list price and still gain 20% ; 
find the list price of the goods. 


11. It costs $36.18 to insure a store at 3%; find the face value 
of the policy. 

12. A schoolhouse costing $9500 is to be built in a district whose 
property is valued at $1,920,000; find (a) the rate of taxation, 


(b) the amount of tax to be paid by a man whose property is valued 
at $6500. (No allowance for collection.) 


276 FROM EXAMINATION PAPERS Written 


26.7 — 11.80 +6.45_ 
3 x 3t x 0.72 
2. The diameter of a bicycle wheel is 28 inches. Find the num- 
ber of revolutions it makes in going a mile. 


1. Simplify 


3. Find the number of square yards in the entire surface of the 
four walls and ceiling of a room 18 feet 6 inches long, 12 feet 4 inches 
wide, and 9 feet high. 

4. If 4% bonds to the amount of $8000 face value are bought 
at 924, find the cost of the bonds and the rate of income on the 
investment. 

5. Find the interest of $465, at 5%, from May 1, 1904, to 
Jan. 15, 1906. 

6. Bought U.S. 4% bonds at 1153 (brokerage 1%) to the amount 
of $5000 face value. Find the annual income and the rate of interest 
on the investment. 

7. Find the cost of four sticks of timber, each 8 inches by 10 
inches and 30 feet long, at $15 per M, board measure. 

8. Find the cost of the following : — 

78 boards 13 ft. x 16 in. x Zin, at $16.50 per M. 
18 joists 10 ft. x 4 in. X 3 in., at $18.75 per M. 

9. At what price must 4% stock be bought so that the invest- 
ment may yield 5% ? 

10. A dealer buys 6 cords of wood at $4 a cord, and 8 tons of 
coal at $4.50 a ton; he sells the wood at 80 cents a cord foot and 
the coal at 50 cents a hundredweight. Find his entire gain. 

11. Find the cost at $17.50 per M of 35 3-in. planks each 22 feet 
long and 16 inches wide. 

12. What will it cost to carpet in the most economical way a 
room 36 feet by 20 feet, with matting 27 inches wide, at 45 cents a 
yard ? 

13. Two successive discounts of 15% and 10% reduced a bill to 
$489.60 ; what was the original bill ? 


Written FROM EXAMINATION PAPERS OT 


d4—2x241 
0.125 + 0.005 — 12) 


2. If 240 lb. of sugar are sold for $19.20‘at a gain of 28%, 
what was the cost per pound ? 


1. Simplify 1+ 


3. How long must a ladder be to reach a window 15 feet high, 
if the foot of the ladder is 8 feet from the house ? 


4. A grocer buys 20 bushels of potatoes at 75 cents a bushel, 
and sells them at 30 cents a peck; find his entire gain and his gain 
per cent. 


5. On January 1, 1904, Edward ‘White of New York sold to 
Charles Holt for cask 1600 yards of flannel at 374 cents a yard, 240 
yards silk at $1.624 a yard, and 1500 yards cotton at 81 cents a yard. 
Make out the Peeaised bill in proper form. 


6. If cranberries are bought at $4 a bushel, at what price per 
quart must they be sold in order to gain 20% ? 


7. How many rods of fence will be required to inclose a square 
field containing 2 acres ? 


8. A man bought a farm of 196 acres for $9800, and after spend- 
ing $980 for improvements, sold the farm at $66 an acre. What 
was his per cent of gain? 


9. What income will be derived from antler $ 14,060 in 31% 
bonds purchased at 873, brokerage 1% ? 


10. How many cubical blocks, each edge of which is 4 of a foot, 
are equivalent to a block of wood 8 feet long, 4 feet wide, and Z feet 
thick ? 


11. A commission merchant sold 744 bushels of wheat and sent 
his employer $527.31, retaining a commission of $30.69. Find the 
rate of commission and the selling price of a bushel of the wheat. 


12. Find the net proceeds of a note of $500, payable in 90 days 
without interest, if discounted at a bank at 6%, 40 days after date. 


278 FROM EXAMINATION PAPERS Written 


1. Find the cost at 16¢ a square yard, of plastering the walls 
and ceiling of a room 18 ft. by 16 ft. and 12 ft. high, allowing 75 
square feet for openings. 


2. Find the cost at $15 per M of 75 pieces of lumber each 14 ft. 
by 16 in. by 1% in. | 
3. The perimeter of one square is 12 inches and that of another 


is 16 inches; find the perimeter of a third square whose area equals 
the area of both. 


4, A merchant bought 351 bushels of wheat for $234; he sold 
half of the wheat at a gain of 15% and the rest at cost. Find the 
average gain on one bushel. 


5. A 4-months note for $735 dated May 16, 1904, drawing 
interest at 5 per cent, is discounted at a bank at 6 per cent two 
months before maturity without grace. Required the proceeds. 


6. How many cords of wood can be stored in a shed 16 feet long, 
12 feet wide, and 6 feet high ? 


7. A man sold a carriage for $207 thereby gaining 121%; how 
much did he gain? 

8. Find the cost of plastering the walls and ceiling of a room 
16 feet by 9 feet and 12 feet high, at 38 cents a square yard, making 
an allowance of } for openings. 


9. A merchant marks an article $6, but sells it at a discount of 
10% for cash and gains 20%; find the cost of the article. 


10. Bought 18,970 lb. of hay at $9 a ton, and 12,580 lb. of straw — 
at $7 a ton; sold the hay at 75 cents a hundred pounds and the 
straw at 60 cents a hundred pounds; find the entire gain. 


11. Find the cost at $50 an acre of a rectangular field 1650 feet 
long and 825 feet wide. 


12. Find the cost at 35 cents per cubic yard of excavating a 
trench 6 rods long, 14 yards wide, and 1 foot 6 inches deep. 


Written FROM EXAMINATION PAPERS 279 


ar foe 
1. Simplify + 

2. Find the amount of $1357.63 at 51% simple interest from 
June 1, 1902, to Dec. 13, 1904. 

3. A speculator buys bonds whose par value is $10,000 at 1133 
and sells them at 115}; how much does he gain if brokerage is 1 on 
each transaction ? 7 

4. Find the square root of 0.729 to three decimal places. 


5. A person failing in business owes $10,800 and has property 
worth $7200; what will a creditor receive whose claim is $180? 


6. Divide the sum of four thousandths and four millionths by 
their difference, extending the result to four places of decimals. 


7. How many shares of stock at 4% discount can be bought for 
$3076 if the broker charges 1% ? 

8. A person borrows $100, and at the end of each year he pays . 
$ 25 to reduce the principal, and pays interest at 4% on what he has 
owed during that year. How much does he owe at the end of 5 years? 


9. A man sold two horses for $124 each, on one he gained 20%, 
on the other he lost 20% ; find the whole gain or loss. 


10. Change 1824 to its lowest terms. 


11. The sides of a rectangle are 8 ft. and 10 ft.; find the diago- 
nal to three places of decimals. 


12. George Dent gives you to-day a note for $480 for 3 months 
without interest; write the note and find the proceeds if it is dis- 
counted to-day at a bank at 6%. 


13. What is the middle minute of a calendar year ? 


14. A merchant gained 121% by selling 48 yards of silk for $4.50 
more than cost; find the cost of a yard of the silk. 


15. Sold 2 of aton for ? the cost. Gain or loss per cent ? 


il » 
een 
id a = 


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DEFINITIONS 


These definitions, arranged alphabetically, are given here mainly for reference. 


They may be 


used, if teachers desire, for review purposes. 


Acceptance. The formal agree- 
ment by signature of a drawee to pay 
a draft according to its terms. 

Acute Angle. 
a right angle. 

Addend. <A number to be added 
to another. 


Addition. The process of combin- 
ing numbers, two by two, into one 
sum. 


An angle less than 


One 
transact business for 


Agent or Correspondent. 
employed to 
another. 


Aliquot Part. The quotient of 
any number divided by an integer. 


Altitude. Height. 
straight line perpendicular to the line 
of the base, and extending from it to 
the highest point. 


Amount. The result of addition ; 
in computing interest, interest and 
principal added. 


Angle. The divergence from a com- 
mon point of two lines having different 
directions. 


Antecedent. The first term of a 
ratio ; the dividend. 


Arabic System of Notation. So 
called because it came into Europe 
from Arabia, and was brought by 
Arabs from India. 


Measured by a. 


Arc. 
ence. 


Any portion of a circumfer- 


Area. The size or total contents of 


a surface. 


Assessment. Money collected 
from shareholders in stock companies 
to meet losses or expenses. 


Assessors. Officers who estimate 
the value of taxable property and 
apportion the tax to be raised. 


Bank. A corporation formed to 
trade in money and securities, or for 
the custody and loaning of money. 


Bank Discount. The allowance 
made to a bank by the holder of a 
note for having it paid to him before 
maturity ; bank interest. 


Base. ‘The line or surface on which 
a figure is supposed to stand. 

The number of which a percentage 
is taken. 


Bill. An itemized statement show- 
ing to whom and by whom goods have 
been sold, or services rendered, and 
giving dates, quantity, price, and 
amount. 

Bill of Exchange. A general term 


for foreign or domestic drafts, espe- 
cially for the former. 


Bonds. A series of interest-bearing 
notes of a government or corporation. 


Broker. An agent who buys and 
sells securities or other property. 


Brokerage. A broker’s fee or com- 


mission. 


Capital. Money or other property 
invested in business, 


Charter. A special act of a legis- 
lature setting forth the rights and 
duties of a corporation. 


Check. A depositor’s order for the 
payment of money by his bank. 


Chord. A straight line joining the 
ends of an arc. 

Circle. A plane surface bounded 
by a curve every point of which is 
equally distant from a point within 
called the center. 


Circumference. 
boundary of a circle. 


The perimeter or 


Commission. A percentage paid 
to an agent for transacting business 
for another. 


Common Denominator of two or 
more fractions. One showing the size 
of some fractional unit in which all 
may be expressed. 

Common Factor of two or more 
numbers. A number that is a factor 
of each of them. 


Complex Decimals have a com- 
mon fraction in the numerator, as 
0.274. 

Complex Fractions contain a frac- 
tion in the numerator, in the denomi- 
nator, or in both. 


il DEFINITIONS 


Composite Number. The product 
of integral factors, 1 not included. 


Compound Number. Two or more 
denominate numbers used to express 
one quantity ; a denominate number 
having two or more integral units of 
the same kind of measure, as 3° 5/. 


Compound Ratio. The indicated 
product of two or more simple ratios, 
3:2 
4:85 

Cone. A solid having a circle for 
its base, and tapering uniformly to a 
point, the vertex of the cone. 


as 3:2 x 4:8, or 


Consequent. The second term of 
a ratio; the divisor. 

Consignor. One who sends mer- 
chandise (a consignment) to an agent 
(the consignee) to be sold. 

Convex Surface. The surface of 
a solid excluding that of its bases. 


Corporation. A company author- 
ized by charter to transact business as 


‘a single individual. 


Couplet. The two terms of a ratio. 

Coupons. Interest certificates at- 
tached to bonds. 

Cube. 
faces. 

Cube (Number). The product of 
three equal numbers ; the third power 
of a number. 

Cube Root. One of the three 
equal factors forming a third power. 
Bix 'O DO = Ber 21s 

Curvilinear surfaces 
bounded by curves. 


A solid with six square 


are those 


Cylinder. A solid having for its 


DEFINITIONS ii 


bases equal parallel circles, and having 
a uniform diameter. 


Days of Grace. Three days, in 
addition to the time named in a note, 
allowed by law in many states for the 
payment of a note by its maker. . 


Decimal Fraction. One or more 
tenths, hundredths, thousandths, etc., 
of an integral unit. 


Decimal Fractions, or Decimals. 
Any number of 10ths, 100ths, 1000ths, 
etc. ; commonly expressed at the right 
of the decimal point without written 
denominator. 


Decimal Point. A period used 
after ones and before tenths. 


Decimals. Decimal fractions writ- 
ten after the decimal point, without a 
denominator. 


Decimal System of Numbers. 
A system in which ten units of any 
order make one unit of the next higher 
order. 


Degree. A 860th part of a circum- 
ference; or, in measuring. aoe a 
360th part of a revolution. 


Denominate Number. One in 
which the unit is a measure, as 3 lb. 


Denominator. The lower term of 
a fraction. It names the fractional 
units according to their size and shows 
into how many equal parts the integral 
unit is divided. 


Diagonalofa Polygon. A straight 
line connecting the vertices of two 
angles not adjacent. 


Diameter. A line measuring the 


shortest distance across a circle or 
square through the center. 


Difference. What must be added 
to the smaller of two numbers to make 
the larger. 


Digits. The numbers for which 
the nine Arabic figures stand. 


Dimensions. Measurements needed 
to find contents. 


Discount. An allowance deducted. 

True Discount. The difference be- 
tween the face and the present worth 
of a debt due at a future time without 
interest. The interest on the present 
worth. 


Dividend. Profits of business di- 
vided among stockholders in propor- 
tion to their shares, 

Dividend. A number to be divided. 

Division. The process of separat- 
ing a number into equal parts, or of 
finding how many times one number 
is contained in another. 

Divisor. A number to divide by ; 
it shows how large or how many 
the equal parts of the dividend are 
to be. 

Draft. An order sent by one party 
to another, requesting him to pay a 
specified sum to the order of some one 
named. 


Sight Draft. One payable when pre- 
sented to the drawee. 
Time Draft. One payable at a speci- 


fied time after sight or after date. 


Drawee. The party ordered to pay 
a draft. 
Drawer. The maker of a draft. 


1V DEFINITIONS 


Duties or Customs. Taxes laid by 
the government on imported goods. 


Duty, ad valorem. A tax of a cer- 
tain per cent of the cost of imports in 
the country where they are bought. 


Duty, specific. A fixed tax levied 
on imports according to weight, num- 
ber, or measure. 


Equation. Two quantities ex- 
pressed as being equal. 


Equiangular. Having equal angles. 


Equilateral. Having equal sides. 


Exact Divisor. One that gives an 
integral quotient, without a remainder. 


Exchange. <A method of making 
payments or collections in distant 
places, by means of orders or drafts, 
without the actual sending of money. 


Exponent or Index. One or more 
figures written above and at the right 
of a number to show how many times 
the number is taken as a factor. 


The first and fourth 


Extremes. 
terms of a proportion. 


Face of Note, Check, or Draft. 
The sum for which it is written. 


Factors. Numbers multiplied to- 
gether in making a product ; commonly 
used as meaning integral factors. 


Figure. A surface bounded by 
lines or a space bounded by surfaces. 

Fraction. One or more of the 
equal parts of an integral unit. 


Greatest Common Factor, Divi- 
sor, or Measure. ‘The largest factor 
found in each of two or more numbers. 


Gross Weight includes the mate- 
rial used in packing. 


Horizontal. Parallel to the plane 
of the horizon. 


Hypotenuse. 
a right triangle. 


The longest side of 


Imports. Merchandise brought 
from a foreign country. 
Improper Fraction. A number 


not less than 1 expressed in the form 
of a fraction. 

Inclined. Neither horizontal 
vertical. 


nor 


Indorsement. A signature on the 
back of negotiable paper. A record of 
payment on the back of a note. 

Indorser. One who puts his signa- 
ture on the back of a note, check, 
draft, etc. 

Insurance. Compensation for loss 
by fire or other disaster. 


Integer. A whole number of which 
the lowest unit is one, not any part of 
one. 

Interest. An allowance to the 
owner for the use of his money. 


Interest, Annual. Simple interest 
on the principal, and simple interest 
upon any overdue interest. 


Interest, Compound. Interest 
reckoned on both the principal and 
the overdue interest added to the prin- 
cipal as often as due. 


Interest, Exact. Interest com- 
puted for parts of a year by taking the 
exact number of days and reckoning 
365 to a year. 


DEFINITIONS Vi 


Invoice. A bill of goods sold. 


Isosceles triangles have two sides 
equal. 


Leakage and Breakage. A dis- 
count for liquors lost from casks or 
bottles during importation. 


Least Common Denominator of 
two or more fractions. One showing 
the size of the largest fractional unit 
in which all can be expressed. 


Least Common Multiple of two 
or more numbers. The smallest num- 
ber of which each is a factor. 


Like Fractions have fractional 
units of the same size and kind. 


Like Numbers have units of the 
same size and kind. 


Line. The limit of a surface. The 


path of a point. 


The one who 
The 


Maker of a Note. 
makes the promise and signs it. 
promisor. 


Market Value. 
open market. 


Present value in 


Maturity. ‘The time when a note, 
draft, or bond falls due and is legally 
payable. 


Means. The second and third 
terms of a proportion. 

Minuend. A number to be lessened. 

Mixed Decimal. A number con- 


sisting of an integer and a decimal 
fraction. 


Mixed Number. An integer and 
a fraction taken together. 


Multiple of anumber’ <A number 


of which it is a factor. 


Multiplicand. One of the equal 
numbers to be combined by multipli- 
cation ; the factor to be repeated in 
making a product. 


Multiplication. The process of 
combining equal numbers, by repeti- 
tion, into one product. It repeats one 
number ‘‘ many fold.’ 


Multiplier. The factor that shows 
how many equal numbers are to be 
combined in the product. 


Negotiable Paper. Notes,.drafts, 
or other written obligations that may 
be bought and sold. 

Net Price or Cost. The price or 
cost after all discounts or charges have 
been deducted. 

Net Weight. 
packing material. 


Weight exclusive of 


Notation. A system of writing 
numbers in figures or letters. 

Note, Demand. One payable at 
the demand of the holder. 


Note, Time. 
specified time. 


One payable at a 


Note, Interest-bearing. One con- 
taining the words ‘‘ with interest.’’ 


Number. That which answers the 
question ‘*‘ How many ?’’; one or more 
units. 

Numeration. A system of reading 
numbers expressed in figures. 

Numerator. The upper term of a 
fraction. It numbers the fractional 
units contained. 


e 


Oblique lines are neither horizontal 
nor vertical. Oblique angles are 
greater or less than right angles. 


Oblong. A rectangle whose length 
exceeds its breadth. 


Obtuse angles are greater than 
right angles. 


Parallel. Extending in the same 
direction, and in all parts equally 
distant. 


Parallelogram. A _ quadrilateral 
whose opposite sides are parallel. 


Partial Payments. 
part of a note or debt. 


Payments in 


Par Value. Face value. 


Payee. ‘The one to whom or to 
whose order a note, check, or draft is 
payable. 

Per Cent. Number of hundredths ; 
units out of a hundred. 


Percentage. The process of com- 
puting by hundredths. The part of the 
base indicated by the rate per cent. 


Perimeter. The circumference of 
a surface or the sum of its bounding 
lines. 


Period. One of the groups, of three 
figures each, counting from the ones’ 
place. 


Perpendicular. At right angles to 
another line or surface. 


Personal Estate. Property exclu- 
sive of land and buildings. 


Plane. A plane surface is a flat or 
level surface. 


Point. That which has position, 


vl | . DEFINITIONS 


but no length, breadth, or thickness. 
The end of a line. 


Policy. The written agreement 
given to the insured by the under- 
writers, 


Poll-tax. A uniform tax on per- 
sons of a certain class. 


Polygon. A plane surface having 
straight sides, commonly more than 
four, 


Port of Entry. A city or town 
containing a custom-house, where U.S. 
duties are paid. 


Power. The product of two or 
more equal numbers as factors. 


Premium. The sum paid for insur- 
ance. Excess of market value above 
par value. 


Present Worth. The sum that, 
at the present time, will pay a non- 
interest-bearing debt due in the future, 
without loss to either debtor or 
creditor. 


Prime Number. A number with 
no other factor than itself and 1. 


Principal. A sum upon which in- 
terest may be allowed. 


Prism. A solid whose sides are 
parallelograms, and whose bases are 
equal parallel polygons. Prisms are 
named from the form of their bases, as 
square prisms, rectangular prisms, tri- 
angular prisms, hexagonal prisms, etc. 


Proceeds or Avails of a Note. 
The sum for which the note is sold. 
Its maturity value less the bank 
discount. Net Proceeds. What is 


DEFINITIONS vii 


left after all charges have been de- 
ducted. 


Product. 
tion. 


The result of multiplica- 


Promissory Note. <A_ written 
promise to pay a specified sum of 
money. 

Proper Fraction. A number less 
than 1; a true fraction. 


Proportion. An expression of the 
equality of two ratios. 


Pyramid. A solid, whose base is a 
regular polygon, and whose sides are 
triangles meeting in a common point, 
the vertex of the pyramid. 


Quadrant. A fourth part of a cir- 
cle or of a circumference. 


Quadrilateral. A plane surface 
having four straight sides. 


Quotient. The result of division. 
Radius. A straight line extending 
from center to circumference of a 
circle. 
Rate of interest. Per cent of the 
principal allowed for a year’s use of it. 


Rate per cent. The number of 
hundredths used in finding a _ per- 
centage. 


Ratio. The relative size of two 
numbers expressed by their quotient. 


Real Estate. Land and buildings. 


Reciprocal ofa Fraction. 1-+the 
fraction, or the fraction inverted. 


Reciprocal of a Number. 1-~the 
number ; the fractional unit expressed 
by that number as denominator, as 3, 4. 


Rectangle. A parallelogram havy- 
ing four right angles. 

Rectilinear. Bounded by straight 
lines. 

Reduction. Changing the unit of 
a number without changing its value. 

Remainder. What is left when 
part of a number is taken away. 

Remittance. Money or negotiable 
paper sent to another. 
Rhomboid. A parallelogram with 
oblique angles. 
Rhombus. 
boid. 

Right Angle. An angle of 90°. 

Roman System of Notation. So 
called because invented and used by 
the Romans. 

Root. One of the equal factors 
forming a power. 


An equilateral rhom- 


Scalene triangles have their sides 
unequal. 

Secant. A straight line that cuts 
a curve at two points. 

Sector. The part of acircle bounded 
by an arc and two radii. 

Segment. The part of a circle be- 
tween an are and its chord. 

Semicircle. Half of a circle. 
Sextant. One-sixth of a circle. 

Share. One of the equal parts into 
which corporation capital is divided. 

Simple Fraction. One having only 
integral terms. 

Slant Height. The shortest dis- 
tance from the vertex of a cone or 
pyramid along the outside to the base. 


Vill 


Solid. A form having three di- 
mensions,— length, breadth, and thick- 
ness. 

Sphere. A solid having a curved 
surface equally distant from the center 
at every point. 


Square. An equilateral rectangle. 
A plane surface with four equal sides 
and angles, 


Square (Number). The second 
power or the product of a number 
multiplied by itself. 


Square Root. One of the two 
equal factors of a square, or second 
power. 

Stock Certificate. A statement 
given by a corporation, showing the 
par value and the number of shares 
owned by a stockholder. 


Stockholders. Owners of the capi- 
tal or stock of corporations. 


Stocks. 
corporations. 
ration bonds. 

Subtraction. The process of tak- 
ing part of a number out of it to find 
the remainder ; finding the difference 
between two numbers. 


Subtrahend. A number to be sub- 
tracted from another. 


Shares in the capital of 
Government or corpo- 


Surface. That which has only two 
dimensions, —lengthand breadth. The 
outside of a solid. 


Tangent. A line touching a curve 
at a single point without crossing. 

Tare. An allowance for the weight 
of boxes, bags, etc., used in packing 
goods. 


DEFINITIONS 


Tariff. The list of dutiable articles 
with the rate assessed on each. 


Taxes. Money raised by govern- 
ment for public uses. 


Term of Discount. The time be- 
tween the day of discount and the day 
of maturity. 


Terms of a Fraction. The numer- 
ator and denominator. 


Terms ofa Ratio. The antecedent 


and consequent. 


Trapezium. A quadrilateral no 
two of whose sides are parallel. 


Trapezoid. <A quadrilateral only 
two of whose sides are parallel. 


Triangle. A plane surface having 
three straight sides. <A right triangle 
has one right angle; an obtuse triangle 
has one obtuse angle; an acute triangle 
has three acute angles. The angles of 
a triangle are together equal to two 
right angles, 180°. 


Underwriters. Insurance com- 
panies. 
Unit. One; any thing used as a 


basis or standard of measurement or 
comparison. 


Vertex. The point in an angle 


where the sides meet. 
Vertical. Relating to the vertex. 
Vertical lines point toward the 


zenith and the earth’s center. 


+ Plus; and; the sign of addition. 
— Minus; less; the sign of subtrac- 
tion, 


DEFINITIONS 1x 


x Times; multiplied by; the sign 
of multiplication. 

+ or: Divided by ; signs of division. 

) In; a sign of division. 


—, /, (as in 13, %). Signs of 
division. 

= Equals, or equal; the sign of 
equality. 


$ Dollar or dollars. 

% Hundredths ; per cent. 

Ct., c., or # Cent or cents. 

@ At (the rate of). 

.’. Therefore. 
() as in (8 +4) x 5= 85) Curves or 
Ne eeassrnde 4 x 5 a Vinculum. 
shows that the numbers inclosed or 


beneath are to be treated as one 
number. 

Vv, the square root of. 

Vaal , the cube root of. 

6%, 785, -06, or 6 per cent. 

2,8, as in 5?= the square of 5 or 25; 
43 — the cube of 4, or 64. 

Dr., debtor. 

Cr., creditor. 

G.C.D., greatest common divisor. 

L.C.M., least common multiple. 

aw. A Greek letter pronounced pi. 
It stands for 3.1416 —, the ratio of 
the circumference of a circle to its 
diameter. 


d 


ie 
4d 


Apa ily te Phenins og: Uy Seg ah) ais Eau AVC pe wh at 


vo Wg wai « At" me ea 


12. 


ee 
oor GD ao w 


ro" 
KOO MAD A Rw We 


ry 


Se 


Page 9 
$45.40. 


. $3800.49. 


$3815.24. 


. $35,751.37. 
. $48,590.80. 
. $11,465.18. 
. $13,729.55. 
. $15,850.62. 
. $16,197.45. 
| $14,581.69. 
. $16,678.86. 
$88,503.30. 
. $88,503.30. 
. $3889.44. 
. $4480.80. 
. $4609.18. 
. $4438.55. 
. $4435.58. 


Page 12 


. $16,654.13. 
. $4881.11. 


$4194.20. 
$7198.54. 


. $12,726.65. 
. $15,138.25. 
. $6668.01. 
. $3960.21. 


$ 9668.11. 


. $14,113.23. 
. $2845.02. 


THIRD BOOK —PART 


12. 
138. 
14. 
15. 
16. 


se 
a) 


—" 
Oo 


OOInaanP ww re 


Soda et pee PD RES lh a OE Ne 


ANSWERS 


$5536.50. 
$ 4245.66. 
$7090.68. 
$1554.18. 
$1290.84. 


Page 14 


. $478.28. 


$ 140.53. 


. $309.52. 


$ 127.78 loss. 


. 256,506. 


860,758. 
850 ft. 


. $620,581,818. 
. $476,500,561. 
$ 657,805,399. 
. $524,955, 950. 
$ 664,426,346. 


Page 16 


$13.44. 

$ 500.78. 

$ 8458.25. 
$15,999.60. 
$7156.52. 
$561.91. 
$44.21. 


. $6368.13. 
ena t| 
. $541.90. 
. $4441.18. 


Page 21 


. 453,456. 
. 2,373,672. 


15,984 ¢. 
35,441 lbs. 
114,163. 


. 62,464 oz. 

. $583,737. 

. 16,308 doz. 
. $38,880. 

. $3096. 

. 8064 gts. 

. 6574 ¢, 

. 129,022. 

. 4214 oz. 

. 29,488 posts. 
. $15,584.73. 
. $226,645.44. 
. $62,652.55. 
. $1484.28. 

. $8741.25, 

. $44,846.50. 
. $1985.75. 

. $4984.00. 

. $3431.25. 

. $3831.36. 

. $2277.45. 

. $8936.28. 

. $6208.61. 

. $9660. 

. $14,456.25. 
. $2259.84. 


34. 
35. 
36. 
37. 
38. 
39. 
40. 
41. 
42. 
43. 
44, 


16. 
17. 
18. 


O or iB © o +2 


$ 34,320.75. 
$12,652.12, 

$ 1769.93. 

$ 141.00. 

$ 230.55. 

$ 4676.25. 
$832.48. 
$174.06. 
17,280,000 rds. 
134,928 sq. in. 
1,555,200 sec. 


Page 22 


. $6471.36. 
: $19,849.83. 


973,000. 


. $316.80. 


$335. 


. $1850. 


Page 26 


. $67.00. 
. $90,817. 
. $82. 

. $825.50. 


“5 ey Goa) gs) cS) 


, 81994. 


, 287238. 
. 807144. 
, 276841. 
. 228621, 
. 290444. 
, 202825. 
. 18992. 
. 402688. 
. T5128. 
, 2915182 


269° 


. 1483 ; 244, 
. 1232; 244, 


1411; 70. 
560 ; 209. 
991; 350. 
719; 32. 


. 810; 754. 


563; 50. 


. 2148; 258, 


508 ; 868. 


, 484: 424, 
. 873; 872. 
. 701; 900. 
. 1346 ; 190. 
. 1130; 125. 
. 1210; 288. 
, 1435; 238. 
. 2258 ; 368. 
. 1858 ; 354, 
, 417; 82, 


eS ee ne 


ANSWERS 

. 2304; 159. Page 34 

eee 1. 63.88 + mi. 

, 2477 ; 356. 

. 307; 262. bee 

} 2.405712 

. 989; 802. 

ie 3. 18%. 

. 286; 840. 4. $2.25. 
Page 31 i ae 
562 7. 160,000 g. 
$350 gain 8. $63.39. 
$ 5265. 9. $996 gain. 
20 bbl 10. $2.50. 
$0.75 
2.10 Page 36 
$402 2. $22.50. 

4. $98.50. 
Page 32 6. $482. 
$130 gain. 7. 4 as long. 
$5750. 8. 6 da. 
8 hrs. 9, 9 1225; 
225 da. 10. 1625. 
$ 52.50. 11. 2052. 

_ 983 mi. 12. $1.50. 

. $15,000; 13. Hans. 
$ 2500. 14. $4. 

. $15.75 gain, | 15. 386 mi. ; 

. Exp. ;. 234, 84 mi. 

| 29, at. 16. $56.25. 

shou. Page 37 

Led oillie 
TEESE 2. 1123 min. 

. 2640. 3. 805 in. 

« 1i,T4l: 4. 2699 sq. in. 

. 15,924. 5. 232 cu. ft. 

. 15,522. 6. 43 pt. 

_ 1,206,060. 7. 1200 rd. 

. 32,616. 8. 224 qt. 

. 8690. 9. 467 hr. 

. 11,466 ft. 10. 1560 sq. rd. 

_ 10,710 Ib. 11. 147 oz. 


. 27,600 lb. 

. 296 qt. 

. 420 mi. 

. 588 min. 

. 15,887 cu. in. 
. 89 gal. 

. 93 Ib. 

. 650% cu. yd. 
. 9337 hr. 

. 67% yr. 

. 6144 bu. 

. 128§ cu. yd. 
. 108 gal. 6 gi. 
. 853 da. 

. 26,000. 
ape 

. 6022 cu. ft. 
. 40 lots. 

. 880. 

. 26662. 

. 2400. 


Page 40 


. $15.40. 
. $2.50. 
. 866 5  S2 awk 


2 da. 


. No profit. 


$ 28.67. 
100 bbl. 


. $158.48. 


4 wk. 


. $426.40. 

. $10,590. 

. 15,840. 

. 4162. 

. 92,795,826. 


Page 42 


355 
oe 


» 81d, 


or 
Co jo of Clo * 
Bip ° al 


by 


ee CO OD dH H, 


OHIHAP WN 


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Pree 
wore © 


Colts BIH! cop alco HI cco 
wie Olt alto oolmr colt ® 
. ° e . 


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ANSWERS 3 


. 6874. 25. 194. Page 59 
. 7948. 26. 75. i 
. 8423, 27. 16293. 2. $52.31, 
. 166. 28. 2 3. $391. 
29. 18256 4. $445. 
Page 51 30. 3. 5. $0.165+. 
. $160.78. 81. 71907, 6. $3.63. 
EO weale 32. $4. 7. $375. 
. $173.96. Socata: 8. $6.00. 
$ 2013. $4. 22. 9. $19.01. 
. $33.91. 35. 3. 10. 3437 mi. 
; eats Page 57 11. 160 mi. 
° F e Oden 
ee 1. 3,78, 12, 12735. 
3.0 2. 11 13. 147, mi. 
aa Bi 
Page 52 3. 125. Page 60 
: 4, 1149. 
io 5. 148%. aes 
$ 20.25 ee 2. 595. 
68. cet 8. 9575 A 
11 cd Ae 4. 10 lb. 
bo" 5 os 5. 3190 
og 1g A Peps 6. 18}. 
18 10. 13. oan 
$ 15 11. 5, ic O04 
8. 185 A 
Leto. aaa © 
; se $0.52. ie *. 9. a 
14. 2. By as 
. $149.50. te 11. 6441. 
2. 48423. Page 66 
Page 53 3. 61043. 1. $9564.88. 
2, 4. 102335 2. 149 
$. 5. 797% 3. 10,235 steps. 
5, 6. 20412 4. 1440. 
as 7. 6644 5. 28. 
a 8. 1115, 6.43, 
= 9. 15335 8. Apr. 14 
fe 108 21772. May Ist. 
25 11. 44324. 9. 14 
Fie 12852-04— 10. 1792. 
56h. 13. 11,352, Ib. 11. $833.38. 
B, 14. 161 ft. 12. 374 ¢; 26; 29%. 


CoH wD Quah owr 


Qapowr 


Page 68 


. $632.76. 


$553.80. 


. $21.46. 


$ 25.66. 
$39.56. 


. $30,700. 


Page 69 
$111.17. 
$38.40. 


. $11,424.29. 


$6198.45. 


. $5255.57. 


$811. 
$51.60. 


. Sec. $15.03. 
. $22,076.28. 


Page 70 
$3.99. 
$6.50. 
$4.35. 


. 800 boxes. 


$2.67. 
337; 
1,89012 Ib. 


2 


vee 
$2.81. 


. Fy; $100. 
. $4105. 

. 44 da. 

. $201.92 ; 


$276.92. 


. 80; 18,750. 
. rh 


. 20 bu. 


Page 75 
I 


. 206.568. 


_ 
So 


- 
= © 


© OI DAP wo 


go ED TR oO 


OCowtkoanPrP wwe 


Po oO 


. 235.722. 
. 21.3725. 
. 22.382589. 


700.108. 


. 680.40235. 
. 234.695. 
. 25.1429. 
. 222.585. 
. 128.27114. 


II 
1.74. 


. 1.5086. 


31.18. 
8.774. 
3.749. 
0.3976. 
1767; 


» 1.5806. 
. 27.926. 
1). DAe 

. 5.898. 

. 2.5416. 
. 23.8852. 
. 8.557. 


Ill 


, aDO.O Cs 


47.252. 


. 203.8074. 


63.045. 
185.41. 


. 44.5387. 


226.472. 


. 396.3544, 
. 152.807. 
.orkeus 

. 23.5287. 


IV 


. 182.62. 
. 1.25412. 


2.886. 


. 7958.2, 


ANSWERS 


Ss 


pa gcd as IST 


SOW IH TP ow 


6. 
0.235. 
0.162. 
0.0163. 


. 1.63. 


Page 79 
3600. 
0.289. 
78.4. 

0.39. 
70.5. 
113.6. 
$8.9125. 
640.0287. 


. 55.1286. 
. 3560. 

. 0.5834, 
. 0.5625. 
. 0.2662. 
. 0.4284. 
. 0.5558. 
. 0.2334, 
. 1.0625. 
PAW hee 
. 0.93883. 
. 0.976;f,. 
. 0.26025. 
, 2.520%. 
. 1.62284. 
. 1.8714. 
. 0.17528. 


35. 
36. 
37. 


1.12. 
0,061; 62%, 
78 %. 


Page 81 


1. 10,400; 12,800; 


8400 ; 8400. 


. $1.15; $138. 
$e 
, 8756.222 ft. 


100 mi. 


. $1,840. 

. $728.89, 

. 90 sq. in. 

. $115,520.98. 
. $180.60. 

. 10.84875 ed. 
. $635. 


Page &3 


$ 147. 
$ 87. 

$ 64, 

$ 1000. 
$ 67.67. 
$ 4.00. 
$ 1.88. 


. $1.87. 
. $3.72. 
. $9.38. 
. $38.26, 
. $94.50. 
. $11.68. 


Page 86 


. 86mi. 28,040 A. 
. 1888 sq. ft. 

. 45 485 sq. rd. 
. 78,135$ sq. ft. 
. 43,560 sq. ft. 

. 2721 sq. ft. 


CO OID a 


SHOR HVE 


_ 


. 217,800 sq. ft. | 
. 6754 sq. rd. 

~ [Lp A; 

. $3411.50. 

. 73750385 sq. rd. 


Page 91 
. 600; 38}. 

1020; 

. 84 sq. yd. 
. 629, 

. 4A, 

. $3482.50. 
. $180. 


. 633,600. 
. $1.20. 
. $17.50. 
. 125 ft. 


Page 92 

21/6386); (BG. 

ugg as “hse BQ 3 
$ 61.25. 

5; 333. 

$ 70. 

$ 26.67, 

. $28.35. 

. $258.90. 

. $24.83. 

. $90.92. 


Page 93 

. 2155 sq. ft. 
770. 

14, 

. 1053; 2850. 
26136. 

70. 

1isq. ft. more. 
. 713 sq. yd. 


ANSWERS 
Page 95-96 Page 101 
. $4098.60. 2. 256 sq. in. 
. $300. 3. 22 sq. ft. 
. $604.08. 4. 90°. 
. $9387.50. 5. 465 sq. in. 
. $1850. 6. 743 sq. in. 
. $2559.38. 7. $2756.25. 
. $1728. 8. 3307%% sq. rd. 
. $2245.82, 9. 3 as large. 
. $1975.59, 10. 714 sq. in. 
. $1447.88. 11. 9. 82 sq. ft. 
. $937.20. 12. 16,500 sq. ft. 
. $1929.60. 13. 174 sq. ft. 
. $272.68. 14. 3,484,800 sq. ft. 
. $332.86, 15. 1534 sq. ft. 
. $57.00. 16. 50 sq. yd. 
. $391. 17. $256. 
. $185. 
, $256.63, Bede 
. $320. 16. 62.832 ft. 
. $1593.38. 17. 65.2535 ft. 
. $42.27. 18. 565.488 ft. 
Page 99 19. 1.48 ft. 
20. 51.05 in. 
. 360 sq. ft. 21. 1.19 ft. 
. 150 sq. ft. 
. 13 8q. ft. Page 104 
ah ihe 6. 37.6992 ft; 
Pa ee an 113.0976 sq. ft. 
. 69753 sq. ft. A ft. « 
1948 aq, ft 1. 31,0992 Ite; 
BTR aq, 9d. 118.0976. 

4 é 8. 31.8309 ; 
bs ve 795.2269. 
iit cea 9. 7.95; 198.74. 
- 15 sq; ft. 10. 706.86 sq. ft. 
ae ge cuhs 11. 1385.45 sq. ft. 

Page 100 12. 12,732.4 sq. in. 
. 932 sq. ft. 13. 1590.4385. 
. 10,560 sq. ft. | 14. 855.30 sq. rd. 
. 11} sq. ft. 15. 5026.56 sq. yd. 
. 38 sq. ft. 16. 928 + sq. ft. 


. 51 — acres, 
. 1154.1176 sq. 


Tu, 


. 104,062,358 sq. 


ft. 


. 7238.246 sq. in. 
. 5944.69 sq. ft. 


Page 108 


T 


5 


. 18.8496. 

. 234.44 ft. 

. 9685.84 sq. ft. 
. 10.2744 sq. in. 
. 632%. 

. 939.2928 sq. ft. 
. 6043 %. 


Page 110 


. 216 cn. in. 

. 512 cu. in. 

Y Wicuait 

. Lizgsieaaac: 
. 1000 cu. yd. 
. 8000 cu. in. 


Page 111 


+ LOOSCH a1: 

. 400 cu. in. 

on | sues pa oe 

s L28OlCus th 

. 4.5 cu. ft. 

. 4608 cu, 1s: 

. 11,3832 cu. ft. 
5 OOO CUS TE. 

. 1772 cu. ft. 

~ a0 Cuwin’s 


300 cu. in. 


. 96 cu. yd. 


. t4-cu. ft. 
z 63 


oO 


4° 


Page 112 


. $18. 
. $100. 

. $112.50. 
. $19.68. 
. $29.30. 
. $5.36. 

. 320 ft. 


Page 113 


LOS it: 


120 bd. ft. 
10 bd. ft. 
37.5 bd. ft. 


. 256 bd. ft. 
. 96 bd it. 
. 140 bd. ft. 
eal Baits 
5-216 bd. ft. 
eo dnt. 


Page 114 


an: 


. 486 cu. in. 


600 cu. in. 
1536 cu. in. 
8 in. 


Pe LOrain: 

ipa ae 

. 114 sq. in. 
. 248 sq. in. 
. 468 sq. in. 
. 544 sq. in. 
. 848; 82. 

. 502; 884. 
. 576; 224. 


Page 116 


. 502.656 cu. ft. 
. 752.0256 gal. 
HO 2Gs a Clad be 


srt 


rf bua 


18. 


ee 
- © 


Po Oo 


Doan wr 


ANSWERS 
Page 117 4. $133,650. 
. 192.9376. 5. 7 ft. 
$ 13.96. 6. $2212.50. 
336+. 7. 21,780 cu. ft. 
. 109.956 sq. ft. | 8 $192. 
9. $5.40. 
Rage sit 10. 22050. 
24; 11. Lecomte 
Ne 252 cu. it. 
78 sq. ft. Page 121 
2 sin.: 1. $50.68. 
. 120 ft. 2. 10,9393 Ib. 
3 yd. 3. $26.98. 
. 5442 ft. 4. 1565.44 T. 
. 26 in. 5. 37.6992 bbl. 
eA tb 6. 603.1872 sq. in. 
. 9 in. 7. $276.67. 
. 96 rd. 8. $5760. 
. 20 in. 9. $476.80. 
. 62,500 sq. ft. | 11. 122%, 
. 160rd; 12. $92.80. 
418 rd, 
6 in. by 18 in. Page 122 
1. 0.36. 
Page 119 2 909. 
$ 10. 3. $6106.88. 
. 4 days. 4, 14213. 
6 in. 5. 13¢. 
12 ft. 6. 1 to 1000. 
12 in, 7. $17.81. 
4 ft. 8. 630. 
. 80 in, 9, 84min. 
1} ft. 10. 4950 ft. 
, ao tb. 11. 85 yd. 
. Gin, 12. $27.06. 
- 660 ft. 13. 500 lb. 
Page 120 Page 124 
. 86 in. 1. $10,000. 
. 184,0784 gal. 2, 433. 
. $48595. 8. 45,375. 


10. 
ik 
12. 


— 
i=) 


OOD Tw 


OWMWIAIHTPR WDE 


CoOtInAanPhwO DH 


Map Veen st 
. 4 p.m. May 31. 


$2822.40. 


4 


$ 63.25. 


. $51.84. 
10. 
‘be 
12. 


$17.28. 
20539, 
29,538. 


Page 126 


. 152.210. 
. $4.65. 


$ 8320. 


. $287.10. 


$ 297.60. 


. 25% loss. 


$55.04. 


. $345. 
. $68.25; 


$121.50. 
5%, 
$1808; $7.53. 
208, 


Page 128 


. $133.35, 

. 54,32. 

. 2237 sq. yd. 
. 594 cu. yd. 
- 624%. 


#ishn 
$79.82. 
2 or 831%, 


. 561%, 

. $8320. 

. py or 10%. 

. $4.60. 

. $4095.24. 
36 

“57 G2 


. 42, 


14. 


= eS 
Oo ce -F co 


OI Qa 


oR ww 


ANSWERS 


THIRD BOOK — PART II 


—_ 
YPYEH SS HAD 


— 


Page 136 . $467. 14. $1241.67. . 162. 
. 1419.4 bu. . $3125, 15. $12,000. » 2094 
$ 2958, . 66 gal. 16. 364 %. Tose aie 
. $337.50. AQT yd. 17. $613.97. . 34 more is 
. 4301 bu. corn. | 8. 250,000 ; gained by 
3542 bu. oats. 105,000. Page 140 buying for 
4807 bu. wheat. . 1900; Te ao $ 4 and sell. 
. 985% T. . $950,000. 2. 960. ing for 
_ 58.8 mi. . 150,000,000 sq. | 3. 2818. $ 4.80. 
. 955% A, mi. 4. 40 A. . $9. 
ao Ad: . 656. 5, 92%. . 84, 
. $209.25. . $251,940. 6. $1728. . Loss $100. 
$ 51.19. . 2032. 7. 565%. - Loss 20 %,. 
. 100 to 1. . $1175. 8. 225 cd. . 145.4545-4. 
. $56,000. 9. 3%: 
. $560. Page 139 10. 7800 T. Page 142 
. $4384. . Alike profit. lis 45 1. $4.80. 
SiO taal. 122 189° 2. $72. 
Pages 137-8 | 3, 254. 13. 138%. 8. $5568. 
ieee . 584%. 14. $9600. 4. $6000. 
96 %. 5. 45 %. 15. 53. GP ea ie 
30,000 ‘T: 6. 95%. 16. 3456. 6. 300 A. 
. $17,634.37 ; 1 LOES, 17. 3.8+ % 7. $47,000. 
4559, 8. 4; 3800; 2%. | 18. $4500. 8. $2000. 
32 %,. 9. 6; 1600; 4%. | 19. $72.90 es da 
$ 21.25. 10. 112; 831%; | 20. 35 10. $1.60. 
. 4469, 163 ¥. 11. $3.50. 
60 %. Diode 1A0. 33): Page 141 
173%. 12. 381%; 381% ;] 1. $6500. Page 144 
. 46,947 —. 25 %,. 2. $24,640. 1. $96. 
$ 963. 13. 625; 2000; | 38. $60; $72. 2. $48. 
$ 635. 1000. 4, 331%. 3. $32. 


= 


10. 


SOD AUD TP o 


$30. 
$ 30. 
$ 35. 
25 %, 


. $20 or 25%, 
. 20%, 


162 %. 


. 142%, 

. $870. 

gS 781, 

. $5000. 

. $50,000. 


Page 145 


. 183% or 144%. 


$10. 


. 20%. 
. $48,000. 


$ 50,400. 
$140. 


Page 147 


. $44.80. 


$ 137.60. 
$ 28.08. 
$ 5.88. 

$ 298.54. 
$375. 


. $104.99. 
. $125.16, 


Page 148 


$8.71. 
$9.92. 


11 


ANSWERS 
. $1.56. Page 152 
SLi. 1. $14.49. 
. $1.36. Ayes 
- $3.19. 8. $17.09. 
- $20.88. 4. $7.99, 
. $11.68. Rares 
poe aL 6. $37.50, 
+ $0.05, 7. $13.24. 
inayre: 8. $4.61. 
9. $21.85. 
- $10.67. 10. $166.45. 
- $15.58. 11. $1.89. _ 
sgt ee 12. $1.67. 
- $14.21. 13. $49.80. 
- $6.48. 19. $88. 
. $1.90. 
. $4.09. Page 153 
soaks Lie 
: | 6. $4.93. 
Page 150 18 Oo LU. 
‘it en 8. $7.76. 
. $7920.11. 9. $11.06, 
‘dean 10. $16.77. 
ene 11. $29.59, 
ncn 12. $160.93. 
$ 214.28, 
. $92.52. Page 154 
. $1187.25. 1. $26.79. 
. $483.69. 2. $759.54. 
. $18.48, 8, $540.11. 
. $1266,663. 4. $15.96. 
5. $900. 
Page 151 6. $540.08. 
Lb yro2lida: 7. $234. 
. 3 yr. 2 mo. 6| 8. $60.67. 
da. 9. $25.20. 
. 2 yr. 10 mo. | 10. $3.15. 
21 da. 11. $3.47. 
_2 yr. 1 mo. 3 | 12. $97.99. 
da. 13. $147.52. 


14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 


DD dD KF KR KR KB RK BS RB eS Se 
Hr ooemnt anh woworo co 


wOovon wo 
a oP & 


OTOP wo We 


$4.41. 
$19.44. 
$ 10. 

$ 227.50. 
$746.67. 
$58.90. 
$105.22. 
$ 333.33. 
$1.29. 
$48.95. 
$ 1312.50. 
$ 4.25. 


Page 155 


. $555.21. 


$ 164.68. 
$ 71.35, 
$ 1316.10. 


. $2607.85. 

. $917.59. 

. $5663.92. 

. $96.63. 

. $12,837.98. 
. $265.45. 

. $552.59. 

. $26,614.07. 
. $76.72. 

. $33.77. 

. $921.65. 

. $10,086.95. 
. $267,793.01. 
. $66.52. 

. $804.37. 

. $1396.14. 

. $15.24. 

. $438.90 or 


$ 438.85. 


. $530.78. 
. $445.06. 
. $971.10. 
. $189.24. 


27. 
28. 
29. 
30. 


OO AD TP Ve 


$ 3014.35. 
$ 2853.33. 
$ 114.28. 
$ 449.50. 


Page 156 


. $475.31. 
. $414.57. 


$ 773.44. 
$ 30.51. 
$ 11.20. 
$ 8.74. 


. $121.38. 


} 26.79. 


. $444.01. 
. $38.55. 
. $854.91. 
. $34.42. 
. $20.30. 
. $45.28, 
. $49.23. 
. $125.16. 
. $41.36. 
. $719.29. 
. $33.66. 
. $85.37. 
| $511.25. 
. $82.06. 
. $1170.68. 
. $38.35. 
- $55.89. 
. $27.99. 
| $525.56. 
. $36.83. 
. $356.58. 
- $64.17. 
. $708.15. 
. $49.47. 
. $7.60. 

. $22.14. 
. $83.94. 


36. 
37. 
38. 
39. 
40. 
41. 
42. 
43. 
44. 
45. 
46. 
47. 
48. 
49. 
50. 
51. 
52. 
53. 
54. 
55. 
56. 
57. 
58. 
59. 
60. 
61. 
62. 
63. 
64. 
65. 
66. 
67. 
68. 
69. 
70. 
71. 
72. 
73. 
74. 
75. 
76. 


$ 19.74. 
$78.06. 
$ 16.04. 


$ 840.55. 


$ 12.10. 
$ 56.79. 
$ 38.56. 


$111.18. 


$ 4.22, 
$ 3.67. 
$ 93.02. 


$ 112.36. 
$ 201.56. 


$ 62.56. 
$ 88.49. 
$ 56.79. 
$ 89.32. 
$45.85. 


$ 814.53. 


$ 31.22. 
$ 48.01. 


$ 422.04. 


$ 22.97, 


$ 502.11. 


$ 40.83. 
$ 17.66, 
$ 6.84. 
$ 42.88. 
$ 64,22. 
$ 3.02. 


$ 126.34. 


$ 36.50. 
$ 10.75. 
$ 17.86. 
$ 12.25. 
$ 306. 

$ 17.25. 


$ 107.26. 


$ 10.55. 
$ 11.20. 
$ 14.58. 


ANSWERS 


77, 
78. 
79. 
80. 
81. 
82. 
83. 
84. 
85. 
86. 
87. 
88. 
89. 
90. 
91. 
92. 
93. 
94. 
95. 
96. 
97. 
98. 
99. 
100. 
101. 
102. 
103. 
104. 
105. 
106. 
107. 
108. 
109. 
110. 
111. 
112. 
113. 
114. 
115. 
116. 
117. 


$ 19.36. 
$ 37.12. 
$557.81. 
$ 41.52. 
$ 77.98. 
$ 4.33. 
$ 12.90. 
$ 36.32. 
$ 10.42. 
$ 29.51. 
$ 42.91. 


$ 1216.19. 


$ 28.89. 
$234.17. 
$8.51. 


$ 1412.15. 


$ 51.92. 
$ 121.48. 
$ 13.51. 
$ 540.00. 
$ 27.34. 
$ 54.44, 
$ 8.80. 

$ 15.34. 
$ 71.32. 
$ 516.98. 
$ 66.74. 


$ 1933.70. 


$ 48.12. 
$ 89.98. 
$ 67.24. 
$2.77. 


$ 1952.00. 


$ 827.36. 
$ 53.30. 
$ 17.66. 
$ 11.83. 
$ 64.80. 
$ 38.73. 
$ 16.90. 
$ 23.22. 


eS EE ee Eee 


118. 
119. 
120. 
121. 
122, 
123. 
124. 
125. 
126. 
127. 
128. 
129. 
130. 
131. 
132. 
133. 
134. 
135. 
136. 
137. 
138. 
139. 
140. 
141. 
142. 
143. 
144. 
145. 
146. 
147. 


SOE COLE | O32 OU. CO N05 


$ 20.27. 
$ 102.39. 
$ 186.91, 
$ 17.44. 
$ 13.25. 
$ 46.04. 
§ 4.48, 

$ 19.38. 
$ 16.20. 
96.44. 
$15.10. 
$ 14.88. 
$ 228.99, 
$ 18.47. 
$ 570.65. 
$ 54.85. 
$ 52.08. 
$25.11. 
$ 62.50. 
$ 104.61. 
$ 363.48. 
$ 133.11. 
$ 551.54, 
$ 30.52. 
$117.79. 
$ 146.07. 
$ 53.32. 
$ 34.00. 
$ 580.32. 


Page 158 


. $1900. 


10%. 
$500. 
$1128. 
3.46 9%. 
2000. 
162%, 
49}. 
$1.50. 


- eS 
wore oo eo 


OMIA 


OIA AP wo wy 


cr i oo 2 


. $500. 
. 2%, 
. $70. 
. 44, 


24. 


Page 159 


. $114, 

- $0.25. 

. First 4% or 
$1.20 (better). 


Third. 
$11.70. 
$ 24.26. 
$ 320.10. 
$5.24. 


$240.88. 
. $2390.08. 


Page 160 


. $1400. $ 1425. 
. $10,590. 


$3920. 
73%. 

15 Y,, 

20 9, 
$313.63. 


. $10,397.75. 
. $598.50. 

. $555.58. 

. $675.88. 

. $67.21. 


Page 162 


- $10,000. 


$ 10,000. 
$2000. 


. $5000. 


11%. 
14%, 


. $6857.14. 


© © =I oO 


15. 


16. 


DW OWR TP OWE 


ANSWERS 

. $4000. 10. 7,2 %. 

. $93.75. 11. 100 M. 

. $31.60. 12. 27%, 

. $15,843.75. 

. $28,388.33. Page 167 

Ron 1. $314.93. 

. $2400. 2. $12,000. 

. $1,500,000. 3. $4123.38. 

. 18%. 4. $7600; 

. $50,000. com. $400. 

. $50,000. 5. $16.87. 

6. $9,250,000. 

Page 164 7. $4000. 
$168.50. 8. $30,000. 

. $10971. 9. $6297.63. 
Zo 10. $58.87. 
3%. 
1.77-% Page 168 
219, 1. $8.74; 
12%. $ 428.26. 
144 %, 2. $2750; $2675. 
Si'as % 3. $25; 10%, 
3%. 4. $918.37; 
24, $18.37. 
B’s Com 5. 14%; $1082. 
$12.08; A’s! 6. $1552.80; 
profit $40.42. $67.20. 
Com. 4 %. 7. $450.70; 3% 
Cost $5000. 8. $421.05. 
$ 7783.16. 9. $526.67. 

10. $200.00 

Page 166 9.63 

. $19.50. 4.37 

. 200 bbl. $214.00. 
$30. 11. $19,998.04. 
$4170. 12. $589.20; 
115 bbl. 112+ %. 
$ 39. 18. $3.52; 

. $11,573.75. 2.37+ %. 

. $170.50. 14. $777.65; 3%. 
5%. 15. $207.90; $198. 


16. 


17. 


© 


$1250 ; 
$43.75. 
$787.49 ; 
$15.39. 


Page 171 


. $261.52 ; 


$261.64 
(grace). 


. $931.60 ; 


$ 932.07 
(grace). 


_ $737.08 ; 


$ 737.39 
(grace), 


. $1963.20 ; 


$ 1963.80 
(grace). 


. $801.95 ; 


$802.35 
(grace). 


. $297.57 ; 


$ 297.68 
(grace). 


. $76.50 ; 


$ 76.58 (grace) 
Page 176 


. $780. 
. $3180. 
. $576.31. 


Page 177 


. $455.80. 
. $700.62. 


$ 661.13. 


. $1290.28. 


$ 664.80. 


. $4431.71. 
, $939.84. 
. $110.30. 
. $1755. 


Page 179 


. $300,000. 
. $50,000; 


$ 10,000. 


. $150n$ 1000; 


15% on $1; 
$ 8000. 


- 13%; $0.012 ; 


124, 


. 148%; $1.48. 


$ 33.383. 
$ 2. 


. $66.67. 
me Rice 
. $15.69-. 
. $12.86-. 
. $6.67. 

. $12.56-. 
aby 

. $112.50. 
. $3876.75. 
. $12.30-. 


Page 181 


. 8243.2. 
. $128.65. 
. Specific duty 


- $40 more. 


. $60.75; 34%. 
. 1221% ; $150. 
. $450.80. 

4 be 

. $0.32 gain. 


Page 182 


. $1226.75. 
. $111.40. 


Page 183 


. $78.81. 
. $206.46. 


eo 


PF © DO 


ANSWERS 
. $449.95. 2. Feb. 15/18; 63 
Int. Table. da. or 66 da. 
. $551.91, 3. Oct. 5/8; 37 
. $713.21. da. or 40 da. 
. $367.58. 4, June17/20; 47 
. $877.50. da. or 50 da. 
5. Aug. 14/17; 
67 da. or 
Page 186 70 da. 
. $790.70 6. Feb. 24/27 ; 26 
(grace) ; da. or 29 da. 
$791. 7. Jan. 19/22; 70 
. $713.90 da. or 73 da.; 
(grace); 2 mo. 9 da; 
$714. 2 mo. 12 da. 
. $8.97 (grace); | 8. May 11/14; 66 
$ 8.75. da. or 69 da.; 
2 mo. 6 da. 
or 2 mo. 8 da. 
Page 187 
. $2.89, $522.11 Page 188 
(grace) ; | 1. 63 da. or 66 da. 
$ 2.63, 2. 24 da. 
$522.37, 3. $438. 
: $906.34 4. $994.86. 
(grace); 5. $795.38. 
$ 906.68. 6. $447.65 
. $310.82" (grace); 
» (grace); $ 447.80. 
$ 311.04. 7. $868.45 
. $784.50 (grace); 
(grace) ; $ 868.81. 
$ 785. 8. $971.54 
. $953.28 (grace); 
(grace) ; $ 972.03. 
$953.60. 9. $693.99 
. $712.41 (grace); 
(grace); $ 694.45. 
$ 712.74. 10. $8387.63 
. July 7/10; 27 (grace); 
da. or 30 da. $ 838.09. 


$ 1248.12 


(grace); 
$ 1248.59, 


. $1080. 
. $1063.80. 


$ 1063.26 
(grace). 


Page 189 


. $1223.64. 


2. $500.14 


10. 


11. 
12. 


13. 


(grace) ; 
$ 501.22. 


. $726.92 


(grace); 
$ 726.81. 


. $396.44 


(grace); 
$ 396.18. 


. $981.14 


(grace); 
$ 980.56. 


. $1272. 
. $1240.20 


(grace); 
$ 1239.67. 


. $1214.76 


(grace) ; 
$ 1214.12. 


$ 1195.68 
(grace); 
$ 1195.04. 
9%, 
$ 448.40 
(grace); 
$ 448.265. 
$715.20 
grace) ; 
$ 714.90. 


11 


12 


14. 


15. 


16. 


17; 


I Oao PP Wd 


= 


— 
w rw 


HOODIA R APY e 


$ 949.62 
(grace); 
$ 949.06. 
$ 806.14 
(grace); 
$ 806.47. 
$277.34 
(grace); 
$ 277.53. 
$ 5037.53 


(grace); 
$ 5037.80. 


Page 194 


. $5022.50. 
. $1977.50. 
. $12,000. 

. 180 shares. 
. $68,400. 
Zh, 

. 51 shares ; 


$ 92. 


. 316 shares. 
. 40 shares, 
. $181,250. 


Page 197 


614, 
3 yf, 


. 8% bond. 


423% 


$ 62.59 loss. 


12%, 


. $4875 loss. 
. Equal. 

. $202.50. 

. 80 shares ; 


$ 20. 


. 69724, 
. $40; latter. 


— 
woro o 


18. 


14. 


—_ — pe 
ow 


—_ 
> 


15. 
16. 


S2tanPrh © dD 


= 
SOBAD TP ww pe 


ANSWERS 
Page 203 Page 205 
DOL ep. 1. $1125. 
. $21.56. 2. 5.13 qt. 
. $217.01}. 3. $56.47. 
. $2085.71. 4. 3.278+ %. 
$ 312.65. 5. Loss $407.69. 
be Wes las 6. 28,8, %. 
$ 6185. 7 40857, 
. $1265.25. 8. $1890 net loss. 
. $12.09. 9. $4,800,000. 
. $5.21, 10. Latter $ 27.28. 
’ cae Page 207 
} ane ‘ 18. 300. 
(grace); f 4g. 331. 
$ 87.70. 
20. 80. 
$ 51.14 
21-39: 
(grace) ; 99. 1 
. 6° 
See 93. 8 yd. 
; 24. $20. 
(grace) ; 
$ 193.95 25.° 75. 
ints’) 26. 60. 
Page 204 27. 96. 
_ $250. 28. 65, 
. 0.605%. 29. 43.5. 
$ 150. Oe 15: 
$ 58.80. 8. $378. 
Sain Page 208 
$941.11. 4 aah 3:4, 
. $1886.70. “acme 
WO A150 
1 12Iar213 p 
8. $33.92 
. $1590. 9. 96 
. Gain $14.25. | 15 Nah 
. $1980. i. oe 
¢ ° 0 
; rae 12. 56 men. 
Cerda) 13. $4.80 per bbl. 
$511.57. Page 209 
$ 75. 2. 604 da. 
$ 500. 3. 2585. 


a a 
PO Or CO SO 


13. 
14. 
15. 
16. 
Lis 
18. 


OI AH ow ww ee os 


Oo 


$819. # 
. 8100 times. 
112 


126 mi.: 251 mi. 
(depends on 
rate). 


. 960 bu. 
. $3.40. 
BeBe clei 


Page 210 


. $62.50. 


2.7 mi, 
$2.50. 
$18. 
48 yd. 
14 rev. 
224 da. 


. 18 Meise 

. $126. 

. Of hr, 

. 2223 da, 

. 4285.71 mi. 
. $133.35, 

. 24 A, 


Page 211 


35. 
96. 


. 680. 
10. 
11. 
12. 


441, 
343. 
420. 


Page 213 
23.=. 

26. 

34, 

42. 

45, 

54. 


a 
oP oo 290 


10. 


i 


— 
POO ONDA Pw DO 


. 638. 
FOG: 
5 Yess 
. 84. 


Page 214 
28. 
58. 
92. 


ols 
. dd. 
2907: 


Page 215 
582. 

547, 

636. 

746. 

869. 

2458. 

(28: 

696. 

799. 


. 852. 
Pata e 
. 967. 
. 1074. 
yivaye 
. 1594. 


Page 216 


. 0.9682+, © 


12, 
999. 
93, 


17. 


10. 


ANSWERS 
. 64. Page 217 
. 1.4142+, 1. 8.94+. 
. 0.4472+. 2. 3.214. 
- 0.19864+. 8. 2.53+. 
PELL 2i43+. An S518 35 
28.0178+. 5. 2.68+. 
. 1856. G4. Lie, 
. 30.23824+. Wiehe oa 
. 0.860813+. 8. 2.92+. 
gun 9. 3.06+. 
. 0.559+. « 10. 2.64. 
Moa LI 182: 
. 2.380+. 12. 0.8862+. 
. 9,099+. 13...6.25+. 
. 0,5422+. 14) 8 9 72+. 
i loee2o ths 
. 1.4790+. 15. 0.6. 
16. 2.39+. 
Sule 
0. 8538+. 17. 8:89+; 
me 18. 5.87+. 
3.7249+, 
1004. 19. 8.00+. 
3136. 20. 6.058+. 
7921. 
45.09. Page 219 
0.75. 1. 60 ft. 
0.96. 2. 68 ft. 
6.5. 3.57 ft. 
0.8848+. 4. 115 ft. 
0.9433+. 5. 42.42+ ft. 
4.4121+, 6. 25.61+ in. 
. 28.7210+. 7. 8.607 ft 
a 4.12754; 8. 223.60+ rd. 
0.8. 
0.2529. 
. 43.9590. Page 220 
. 27.9991+. 1338; 
. 15.08. 9. 8.664, 
71420. 3. 24.16+ ft. 
8314; 4521-08 ft: 
282843 5. 73.82+ sq. ft. 


6. 


a 
Hw Oo 2 


= 
KP OO MAD AP wD 


13 


Altitude, 
20357 8 ff, : 
area, 
249.36+ sq. ft. 


. $141.40. 
. 259.8 sq. in. 


Page 221 


~ 29.674 It. 
» 29.64 iti 


13.4 ft. 
8. 


. 25.374 rd. 


67.8+ mi. 


. 1017.8784 sq. 


In. 


. 5.56+, 

. 270.4+ ft. 
2 18.02/46. 
» Leer. 


Page 222 
6.9282+ rd. 


. 43,863 ft. 


5:4, 


. 21.089 rd. 

= 20387 is ite 

. 97.616+ ft. 

. 63.639 ft. 

. 101.98+ ft. 

. 108 ft. by 36 ft. 
. 20.78+ it. 

. 27.12+ ft. 

. 137.08 isqe in, 
. 2368.074 ft. 

. 69.41 rd. 


Page 225 


. 2917 cu. ft., or 


29.629+ cu. 
ft. 


14 


8. 471.4 cu. in. 
4. 1500 cu. in. 
5. 6600 lb. 
10. 96 sq. in. 
11. 384 sq. in. 
12. 62.34+ sq. in. 
13.. 720 cu./in. 
14. S. H.. 16.15+ 
in,; ¢. sur- 
face 887.6+ 
sq. in. 
Page 227 
habe 


Poe 1372 ca. in: 


1 

2 

8. 24 cu. in. 
4. 6 sq. in. 
5 
6 
9 


. 01,6992 cu. TE 


00g 

. 40 sq. in. 
10. 20.1219+ sq. ft. 
11. 93.4626. 
12. 219.912 sq. ft. 
13) (1.05 -y a. 


Page 230 


1. 0.5286. 
2. 0.4764 ; 
0.5236 rem. 


. 285.62 Ib. 

. 18.566+ Ib. 

. 4,188,800,000 
cu. mi. 

. 64. 


ao oa Pf 


mi. 


11. 14.573 lb. avoir. 


12. $74. 
13. 486 oz. 


OID TP wo 


o 


. 38.5104 cu. In. 


D Po 2 


7 

8. 67.0208 cu. in. 
9. 113.0976 sq. in. 
10. 12,566,400 sq. 


ANSWERS 

Page 233 12. 28.2744, 

$ 2700. 13. 18,000 lb. 

res 14. 706.86 sq. ft. 

$ 18.56. Page 244 

195: 1. 847,200 g. ; 

5 

1867.75 lb. 
pele 2. 26.43 HI. 
Be Ee 3. 16.72 sq. mm. 
: ae 4. 1312.359 yd. 
. 1171.874 bu. 5, 8395.38 Sq. rd. 
_ 96 hy. Beane | 
Page 237 7. $10.63 gain. 
8. 960 Ke. 
| $9.25. 
9. 88.9056 Ke. 
. 681.7925+ sq. 
5 Sd: | 10. 2.845184 Mm. 
ee iis Jas 
. 425 sq. ft. Ree te 
138.38 A. 
. 315 sq. ft. 13, 264.17 eal 
. $32.26. a piiea: 
. 124.686. eel 
oy 15. $3.21. 
_ 1.27824 ft. mee aaah OTS 
bed: 17. 7500 m. 
' exe date 18. 1s 220 T. 
A BBS onittme | Seg ee 
Page 246 
Page 238 aay 
3. 12:53:36 p.m. 

1080. 

p 4. 7:15:48 a.m. 
. 6.2882 cu. in. 
d 5. 5:53:20 p.m. 

12.65- in. 

530.146 ec, in. | 8 022282 mil 
hee eae 7. 6:33:20 a.m. 
spear tt * |g 6:25:8a.m. 

ee 9. 11:59:86 a.m. 
169.68+ rd. ; 10 oR oe 

150.40- rd. se viare ee atees 

94.81 11. 12:93:20 p.m. 
fee 12. 3:5:16 a.m. 
. 26.529+. 

PAYOIs Page 251 
. 1607.8125 lb. | 1. $60,000. 
. 14,.9334+ ft. 2. $160. 


_ eae 
FOOD DAHA SP wW POG (Soot Sore A ee 


= 


OHIATh OV 


— pt pe 
On re © 


_— 
» 


819, 


. $21,000. 


6 in. 
$2.60. 
$1.57. 
67,200. 


BEY, 


. 940 bbl. 
. 832%, 


Page 252 


. $33,280; $80 


brok. 


. Dec. 22, 1908. 


$ 148.19. 
$ 153.58. 
36 weeks. 


. $10,844. 


$80. 


. 672 ft. 

Bab bch 

. $346.15. 

. 105,753.6 gal. 


Page 253 


$80. 
$1800. 
$1.88. 
0.927-. 


. 1282 + bbl. 


$0.53. 


. $24 increase. 
. $77.91. 
. $1256.25 ; 


99,243.75. 


. 12,480 lb. 

. $22,000,000. 
. $32.40. 

. 939.84+ cu. in. 
28 7 0Sc 


eT cats bien eeee oe 


ee 
Cr 


OMAR ATP w we 


—_ 
wore © 


—_ 
Po Sa Ee St oe ho 


i 


Page 254 
$379.88. 


. Int. $25. 
. $647.90. 


Page 255 
. $11,848.80. 


. 57823 cu. ft. 


$ 4649.80. 
62%. 

$ 3854.17. 
$ 2172.50. 
43.30 ft. 

. $816.06. 

. 25%. 

. $55.36. 

. $345. 

. $905.42. 


Page 256 


. Latter. 
$ 767.38. 
$ 2250. 
40 ¢, 

30 mi. 

$ 844.95. 
162%, 

$ 59.63. 
$4704. 
$43.20. 

. $42.86 per 


$ 100 share. 


ANSWERS 
12. 3 mo. 6. $34.45. 
. 12h yr. 7. $41.48 more. 
. 6.336 in. 8. $0.133. 
9. 461.8152 cu. in. 
Page 257% | 10. $4936.60, 
ie ie Page 260 
. 280 gal. ; 1. 173%: 
200 gal. 2. First, 72% 
; 32 ft. better. 
. 1368 sq. ft. cy Ls 
. $5.60. ee eG 
- $1050, 5. $156.08. 
ition, 6. 63.8: 36.2. 
. 1143. 7. $0.94. 
Booms JUsep ie ween 
ie 9. $3.24. 
1348 A. 10. 0.816. 
- $310. 11. $9.21. 
$28.80. 12. 11.55. 
13. Increase $15. 
Page 258 14. 608 ; 544, 
- $595. Page 261 
noe 1. 3125. 
. 49:98=98: | 9 107.603, 
ah 8. 336.13+. 
a 4. $12,000. 
30 # per yd. 5. Loss $16. 
See 6. $425. 
te ’ Fhe 7. $302.25. 
3 in, . 10 
9. 200,000 Ib. . aa & to 
. $1279.94. 10. $402. 
- #819. 50. 11. 9.36+%, 
12. $56.53. 
ea 13. 1963.5 sq. in. 
1. 14,9125 %. 14. 140.0616 sq. in. 
2. 18849. 
3. 7.854 sq. ft. Page 262 
4. $0.94. Tees: 
5. $17.67. 2. 70.71- mi. 


OowA sa PE 


= ee 
Wore © 


Oo fF © oO 


15 


. $206.45 ; 


$ 208. 


. $495.08; 


$494.83 
(grace). 


. $2934.37. 
- @BH= 


$16.09 less. 


ba) tds e251: 


588 sq. rd. 


. L. price 


$960 ; 
cost $400. 


. $1481. 

. $26.16. 

. $889.43, 
. $0.86. 

. $25,000. 

. 62%, 


Page 263 


is: 
70+ gal. 


. 389.7+ ft. 


384%. 
60 %, 
$ 632.10. 


. 663 % 

. $94.50. 
. $80. 

. $640.25. 
. $450. 

. $84.31, 


Page 264 


. 1.38084, 
. $518.55. 


48 ft. 


. $555.10. 
. 420.168+. 
. $17.92, 


16 


. $352.837+ - 


7 

8. $3668.75. 
9. $35,000. 
10. 87} ¢. 

11. $58,500. 
12. $2971.25. 


13. 56.568+ rd. 


14. $344.53. 


Page 265 


$ 40.32. 
160 bbl. 
$10.75. 
$ 56.77. 
16 rd. 

. $260.40; 


See Te edie 


$13.02 com. 


. §6.56+ rd. 
. $5.50. 

. $1930.43. 
. EY. 

18. 5%, 


- = = 
woros 


Page 266 
1. $55,000. 
2. 44.74- %. 
3. 542%. 

4. 413,0134. 
5eo Ae 

6. $2.75. 

WY 177%. 

8, 22,8 4. 
9. 4. 

10. 1662. 


11. 3616.037+ bu. 


12. 163%, 
13. 93.81 — rd. 
14. $22.68. 
15. $5190. 


eet 
PP CO WO KH © 


—_ 
(s) 


OO AIA TP ww 


— 
rOoDO SONIA AP OD 


OHOWAHAM Pwr 


ANSWERS 
Page 267 10. Six hund. six 
2, thous. and 
12 ft. fifteen tril- 
50%. lionths. 
80. 11. Nothing. 
. 154.284+ bu, | 12. 14 §¢. 
$ 140.623. 13. $625. 
$ 5.60. | 
$90.56. Page 270 
- 125%, ligbeee 
. $2.625, 2. $67.20 
. $12. 3. $28.80 
. $252.58. 4.4% 17.36- 
. 125 ft. 5. $51,568. 
- $198. 6. 9929.4. 
7%. 62.38376+ min. 
Page 268 8. 1765.17 gal. 
. $4,375. 9. 1:10. 
. 1662 %. 10. $20. 
40 ¢. 11. $5157.43. 
$ 8.27. 12. $4499.25. 
4% 
$ 371.20. Page 271 
$ 40. 1. 0.0162. 
. $105.80. 2. $21. 
. $391.27. 8. 44.74-9. 
. $620.82. 4. 2473. 
- $187.20, 5. 684 ¢. 
. $220. 6. $93.75. 
1.7 33,0803. 
Page 269 8. 10¢. 
, 8213. 9. 12 da. 
810), 10. $283.50. 
8 6150. 11. 32.725 Ib. 
165 ft. 12. 136 cu. yd. 
$ 3761.25. 13. 12 rd. 
. 9662. 
Sai Page 272 
. 6h ft. Lito 
$ 5.47. 2. $54181. 


ee ee 
oo wo KX © 


so 


PDa2Inarronr 


$94.52. 
$418.88. 


. $56,250 5 38% 


$ 25.92, 


. 64 men. 


$8000. 
$76. 


. $377.32. 
. $150. 
. $421.55. 


Page 273 


Sai 
140° 


. 159,155 cu. ft. 


116 ft. 


. Loses $10. 


$96.21. 


. $577.40. 


$386 ; cost 
600 fr. 


. $12.75. 
. 0.02078125. 
. $810. 

. $5700. 


Page 274 


wae 


. Seven thou- 


sand four 
hundred 
eighty-five 
and two 
ninths ten- 
thou- 
sandths. 


. $43.20. 
. $82.08. 


— 


— 
wero 


a 


OOAWR AP ww yp 


. $2007.50. 


126. 
$1337. 
241 bu. 
$2.18. 


. $150. 


Page 275 


22, 
$8625. 
$3978.72. 
662. 

$ 125%, 
$9.45. 
8%. 


. $21.84. 


$7.48. 
$1.80. 


. $4824. 
. $32.18; $4.95 


per thous. 


Qo Pw dD 


ANSWERS 
Page 276 6. 15¢. 
1243. 7%. 71.65+1d. 
. 720.288 +. $720 5. 
874, sq. yd. 9. $560. 
. $7400, 412%. | 10. 1728. 
$39.65. 11. 55%; $0.75 
. $200 income ; per bu. ; $558. 
349701, 12. $495.58 
$12. (grace) ; 
. $24.79. $495.83. 
80. 
oe. Page 278 
. $53.90. 
. $48. 1. $18.29. 
. $640. 2. $36.75. 
3. 20 in. 
Page 277 4. 5¢. 
+o- SRI By ye 
67%. 6. 9 cd. 
Liat, tb Eph 
$9; 60%. 8. $26.18. 
. $1115. 9. $4.50. 


10. 
iv 
12. 


— — — pe 
wOwreo Oo 


14. 
15. 


Sap ketal Nig ed Hine ase 


17 


$88.36. 
$ 1562.50. 
$ 8.66. 


Page 279 
64. 


. $1546.79. 


$ 150. 
0.853 +. 
$ 120. 
1.002. 


. 32 shares. 


53° 
. 12.806 + ft. 
. Variable. 
. July 2, noon, 


or July 2, 12 
p.m. 

75 ¢. 

123%. 


aN 


he a be 


wr. 


ay i oe 


URBANA 


” 
oO 
= 
a | 
= 
ts 
=) 
7 > 
_ 
“a 
cc 
Lhd 
= 
= 
=> 


< 
os) 
i=] 
i) 
o 
_ 
wn 


v003 
STONE ARITHMETIC BOSTON 


TUS 


C001 


THE SOUTHWORTH 


(3.0112 017106359 


